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[EDIT]Woah, you just edited your post beyond belief[/EDIT]
That's still wrong. You use TWO ADDITION PROBLEMS. The question asks for ONE ADDITION, ONE MULTIPLICATION, in TWO SEPARATE EQUATIONS. Sorry for the yelling, but I'm trying to make some sense to you here.
And the cube did violate the equation, because a cubed is a shortening of (x^1 * x^1 * x^1). So it's equivalent to 6 separate multiplication instructions.
That's still wrong. You use TWO ADDITION PROBLEMS. The question asks for ONE ADDITION, ONE MULTIPLICATION, in TWO SEPARATE EQUATIONS. Sorry for the yelling, but I'm trying to make some sense to you here.
And the cube did violate the equation, because a cubed is a shortening of (x^1 * x^1 * x^1). So it's equivalent to 6 separate multiplication instructions.
Now he points out the "flaw inherant in the system"
Alright, N-space it is. This equation is unsolvable to the core unless you can operate inside N-space and then you can pretty much bend the laws of math.
PS: Technically, I didn't break the rules with my cube, "I don't break rules, I just bend them into pretzals"
Alright, N-space it is. This equation is unsolvable to the core unless you can operate inside N-space and then you can pretty much bend the laws of math.
PS: Technically, I didn't break the rules with my cube, "I don't break rules, I just bend them into pretzals"
Okay, well, I don't have a n-space graphing calculator. Good luck! And if you never need any basic modulus arithmetic, just ask. :P
13 [+] 10 = 10
10 * 13 = 130
(10 [*] 13 = 0, but I did 10 * 13)
Basically, to do modulus addition or multiplication, do the problem as with normal numbers, then divide by the modulus and take the remainder . So 10 [*] 3 in modulus 13 would be the remainder of 30/13, which is 4. 13 * 2 = 26, 30-26 = 4. Heh. Or, if the answer is less than (modulus)*2, just subtract the modulus. So 13 [+] 10 is 10 because 23-13 = 10.
13 [+] 10 = 10
10 * 13 = 130
(10 [*] 13 = 0, but I did 10 * 13)
Basically, to do modulus addition or multiplication, do the problem as with normal numbers, then divide by the modulus and take the remainder . So 10 [*] 3 in modulus 13 would be the remainder of 30/13, which is 4. 13 * 2 = 26, 30-26 = 4. Heh. Or, if the answer is less than (modulus)*2, just subtract the modulus. So 13 [+] 10 is 10 because 23-13 = 10.
alright since no one got it and i'm not really willing to part with 50k of precious credits to give to bountybot... i'll give the answer...
x + y = 10
x * y = 130
y = 10 - x
(10 - x)x = 130
-x^2 + 10x - 130 = 0
-10 +- sqrt(10^2 - 4(-130)(-1))/-2
-10 +- sqrt(-420)/-2
-10 +- 2i sqrt(105)/-2
x = 5 + i sqrt(105)
y = 5 - i sqrt(105) <--- didnt show the steps for this, pretty much similar to the one to find x
now, imaginary numbers: i = sqrt(-1) and 2i = -1 and so on
5+ i sqrt(105) + 5 - i sqrt(105) = 10 because the complex part cancels out.
(5 + i sqrt(105)(5 - i sqrt(105)) solve this like a binomial
25 - 5i sqrt(105) + 5i sqrt(105) + (i sqrt(105)) * (-i sqrt(105))
the -5i sqrt(105) and 5i sqrt(105) cancels out.
multiply the -5i sqrt(105) and 5i sqrt(105) in the last part and you get:
25 + (-1)(-1) + 105 <--- i^2 is -1, the other -1 is the - sign. 105 results from multiplying the square root parts.
eventually ends up with...
130
so to recap:
the 2 numbers are
5 + i sqrt(105)
and
5 - i sqrt(105)
x + y = 10
x * y = 130
y = 10 - x
(10 - x)x = 130
-x^2 + 10x - 130 = 0
-10 +- sqrt(10^2 - 4(-130)(-1))/-2
-10 +- sqrt(-420)/-2
-10 +- 2i sqrt(105)/-2
x = 5 + i sqrt(105)
y = 5 - i sqrt(105) <--- didnt show the steps for this, pretty much similar to the one to find x
now, imaginary numbers: i = sqrt(-1) and 2i = -1 and so on
5+ i sqrt(105) + 5 - i sqrt(105) = 10 because the complex part cancels out.
(5 + i sqrt(105)(5 - i sqrt(105)) solve this like a binomial
25 - 5i sqrt(105) + 5i sqrt(105) + (i sqrt(105)) * (-i sqrt(105))
the -5i sqrt(105) and 5i sqrt(105) cancels out.
multiply the -5i sqrt(105) and 5i sqrt(105) in the last part and you get:
25 + (-1)(-1) + 105 <--- i^2 is -1, the other -1 is the - sign. 105 results from multiplying the square root parts.
eventually ends up with...
130
so to recap:
the 2 numbers are
5 + i sqrt(105)
and
5 - i sqrt(105)
imaginary numbers people... quit thinking so hard and think imaginary numbers....
Okay.
╔ + ╙ = 10
╔ * ╙ = 130
Yay! Solved.
╔ + ╙ = 10
╔ * ╙ = 130
Yay! Solved.
incorrect. by imaginary i mean the type of numbers called "imaginary numbers" not just... imaginary numbers that you or i made up...
Okay.
x = 6
x + 4 = 10
x = 13
x * 13 = 130
x = 6
x + 4 = 10
x = 13
x * 13 = 130
x+4=10
x*13=130
4 isnt 13
x*13=130
4 isnt 13
Nice, except for the post above...
"incorrect. by imaginary i mean the type of numbers called "imaginary numbers""
Except any number multiplied by an imaginary number creates an imaginary number as a result. And since the result is 130... not an imaginary number. You've already taken them out of the equation.
If one number were negative and both were imaginary you would end up with a positive number as the result of a multiplication... however, you would not end up with that result from the addition.
yjia2? Please post your answer so we can find out what's wrong here.
"incorrect. by imaginary i mean the type of numbers called "imaginary numbers""
Except any number multiplied by an imaginary number creates an imaginary number as a result. And since the result is 130... not an imaginary number. You've already taken them out of the equation.
If one number were negative and both were imaginary you would end up with a positive number as the result of a multiplication... however, you would not end up with that result from the addition.
yjia2? Please post your answer so we can find out what's wrong here.
em....oki....right...
modulus is how you can solve those "how many quarters, nickels and pence do you need to buy $540912.31 of cheese" problems in three steps.
/me goes back to 6'th grade algerba
Ok, now that I see what yjia2 solution to that problem was...
I agree with anyone in the game, he deserved to be verbally abused if only because of the way he explained it. Because the answer makes no sense when you look at the problem.
The basic question. Find 2 numbers, that when added = 10, and when multipled = 130.
So we have the equations x+y=10 and x*y=130
When we are presented with the solution that yjia2 presents...
x=5+i*sqr(105)
y=10-x
...
We encounter a problem...
5+i*sqr(105)... and anything at all with a i* in it, is no longer a number, but... according to a few year old calc book...
"An expression denoting the set of all possible products iw, where w is an element of the set R of real numbers"
Also, we encounter a second problem..
y=10-x
This is also not a number! This is an equation that will result in a number, and not a number itself.
yjia2? If your wondering why no one got the answer after all that debating, and why everyone said it wouldnt work, its because it really and truly doesnt work the way you set it up.
x+y=10 and x*y=130 is impossible if both answers are supposed to be numbers.
If you do post any more math problems, here, or in the game itself. Make sure its solvable given the rules you present...
I agree with anyone in the game, he deserved to be verbally abused if only because of the way he explained it. Because the answer makes no sense when you look at the problem.
The basic question. Find 2 numbers, that when added = 10, and when multipled = 130.
So we have the equations x+y=10 and x*y=130
When we are presented with the solution that yjia2 presents...
x=5+i*sqr(105)
y=10-x
...
We encounter a problem...
5+i*sqr(105)... and anything at all with a i* in it, is no longer a number, but... according to a few year old calc book...
"An expression denoting the set of all possible products iw, where w is an element of the set R of real numbers"
Also, we encounter a second problem..
y=10-x
This is also not a number! This is an equation that will result in a number, and not a number itself.
yjia2? If your wondering why no one got the answer after all that debating, and why everyone said it wouldnt work, its because it really and truly doesnt work the way you set it up.
x+y=10 and x*y=130 is impossible if both answers are supposed to be numbers.
If you do post any more math problems, here, or in the game itself. Make sure its solvable given the rules you present...
5+i*sqrt(105) is called a complex number. Perfectly valid. I would have answered the same way had I seen it. i isn't a variable, it's the square root of -1, so technically the number is 5+sqrt(-105), which is a constant.
He didn't say they had to be integers, real numbers, rational numbers, whole numbers. They're complex numbers, and the complex domain is important.
He didn't say they had to be integers, real numbers, rational numbers, whole numbers. They're complex numbers, and the complex domain is important.
i said about a million times in my hint stating its complex... and "5+i sqr(105)" is this "imaginary number" (or complex, whichever way you say it"
a complex number consists of 2 parts, the real part and the complex part, the real part is 5, the complex part is 105.
the solutions i presented is
5+i*sqrt(105)
5-i*sqrt(105)
this is known as complex conjugates.
"An expression denoting the set of all possible products iw, where w is an element of the set R of real numbers"
this statement does not apply to the problem as this statement states that it is for real numbers only, which the answers are not.
2ndly this statement is written based on the assumption that i is an undefined (meaning not defined, value varies, etc) variable. where as in my statement i = sqrt(-1)the i used here is the common way of denoting a "complex unit" which is basically sqrt(-1)
y=10-x is not a number because that's part of the algebraic expliaination that i use to find the correct answer, it is simply a different way of saying x+y=10, i changed it to y=10-x because i need to subsitute it into th efirst equation, nowhere did i say that that is actually one of the numbers.
"x+y=10 and x*y=130 is impossible if both answers are supposed to be numbers."
that statement is invalid as i gave you the answer... and it does work. the correct statement is : "x+y=10 and x*y=130 is impossible if both answers are supposed to be real numbers."
as stated before those answers are not real numbers.
and lastly i never said 5+i*sqr(105), i said 5+i*sqrt(105)
a complex number consists of 2 parts, the real part and the complex part, the real part is 5, the complex part is 105.
the solutions i presented is
5+i*sqrt(105)
5-i*sqrt(105)
this is known as complex conjugates.
"An expression denoting the set of all possible products iw, where w is an element of the set R of real numbers"
this statement does not apply to the problem as this statement states that it is for real numbers only, which the answers are not.
2ndly this statement is written based on the assumption that i is an undefined (meaning not defined, value varies, etc) variable. where as in my statement i = sqrt(-1)the i used here is the common way of denoting a "complex unit" which is basically sqrt(-1)
y=10-x is not a number because that's part of the algebraic expliaination that i use to find the correct answer, it is simply a different way of saying x+y=10, i changed it to y=10-x because i need to subsitute it into th efirst equation, nowhere did i say that that is actually one of the numbers.
"x+y=10 and x*y=130 is impossible if both answers are supposed to be numbers."
that statement is invalid as i gave you the answer... and it does work. the correct statement is : "x+y=10 and x*y=130 is impossible if both answers are supposed to be real numbers."
as stated before those answers are not real numbers.
and lastly i never said 5+i*sqr(105), i said 5+i*sqrt(105)
/me 's bs alarm goes off
his answer, while correct, is more or less useless. the question was stated somewhat misleadingly.
while the denotation of the term "number" does include complex and non-real number sets, the connotation generally is accepted to mean real values that can be expressed on a coordinate system consisting of 3 axes (x,y,z) at a given instant in time.
his question would have been better worded as follows
what 2 mathematical expressions can be added to each other with a result of 10 and multiplied with each other for a result of 130.
while the denotation of the term "number" does include complex and non-real number sets, the connotation generally is accepted to mean real values that can be expressed on a coordinate system consisting of 3 axes (x,y,z) at a given instant in time.
his question would have been better worded as follows
what 2 mathematical expressions can be added to each other with a result of 10 and multiplied with each other for a result of 130.
Why is it any more or less useless than any other number, complex or not?
Of course it was slightly misleading; if it were something as simple as linear algebra, what would be so special about the problem? But complex numbers are numbers, you don't have to call them "mathetmatical expressions".
Here's two mathematical expressions which are a solution:
x+y+z^152+5-72+sqrt(-105), and
5+72-sqrt(-105)-x-y-z^152
Of course it was slightly misleading; if it were something as simple as linear algebra, what would be so special about the problem? But complex numbers are numbers, you don't have to call them "mathetmatical expressions".
Here's two mathematical expressions which are a solution:
x+y+z^152+5-72+sqrt(-105), and
5+72-sqrt(-105)-x-y-z^152
a complex number is stated wiht a real part and a complex part. it is not an expression. the real part and complex part should be counted as an single entity.
the point of the question was for people to think outside the box of using real numbers, what'd be the point if i specified specifically that i was looking for a complex number or an expression.
bottom line: i dont care if you thought that the way i asked the question was unfair, i specifically asked it that way because it'd actually serve the purpose of the question. Just because you assumed errornously about my question doesnt mean you get to whine and complain about it. it was MY question, you dont HAVE to answer it, and you dont HAVE to be annoyed even though you had a wrong chain of thought, because that's just what i designed the question to do.
i know there's multiple answers a1k0n, but why the x y and z?
the point of the question was for people to think outside the box of using real numbers, what'd be the point if i specified specifically that i was looking for a complex number or an expression.
bottom line: i dont care if you thought that the way i asked the question was unfair, i specifically asked it that way because it'd actually serve the purpose of the question. Just because you assumed errornously about my question doesnt mean you get to whine and complain about it. it was MY question, you dont HAVE to answer it, and you dont HAVE to be annoyed even though you had a wrong chain of thought, because that's just what i designed the question to do.
i know there's multiple answers a1k0n, but why the x y and z?