sum of square roots

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ChocolateMilk

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Can anyone help me solve this math problem?

The sum of two numbers is 12. The sum of their squares is 78. What are the two numbers?
 
Your subject line refers to "square roots", but the posted exercises refers to "squares". Which is it?

When you reply with clarification, please also include a listing of everything you have tried so far. For instance, you picked variables to stand for the numbers, wrote an equation representing their sum, and... then what?

Thank you.

Eliz.
 
ChocolateMilk said:
Can anyone help me solve this math problem?

The sum of two numbers is 12. The sum of their squares is 78. What are the two numbers?
Click to expand...
Given: x + y = A and x^n + y^n = B.

1--Let x = z + A/2 and y = z - A/2
2--Substitute into x^n + y^n = B and solve for z.

Example: x + y = 14 and x^3 + y^3 = 854
1--x = z + 7 and y = z - 7.
2--Substituting, (z + 7)^3 + (z - 7)^3 = 854
3--Expanding, 343 + 147z + 21z^2 + z^3 + 343 - 147z + 21z^2 - z^3
4--Simplifying, 42z^2 = 168 or z^2 = 4 making z = 2.
5--Therefore, x = 9 and y = 5.
6--9 + 5 = 14 and 9^3 + 5^3 = 729 + 125 = 854.

Try it with your numbers.
 
1,11 : 1,121 : 122
2,10 : 4,100 : 104
3,9 : 9,81 : 90
4,8 : 16,64 : 80
5,7 : 25,49 : 74
6,6 : 36,36 : 72
 
Denis said:
1,11 : 1,121 : 122
2,10 : 4,100 : 104
3,9 : 9,81 : 90
4,8 : 16,64 : 80
5,7 : 25,49 : 74
6,6 : 36,36 : 72
Click to expand...
But the exercise just says "numbers"; it does not specify "whole numbers".

I'll grant you, though: it's the natural assumption (no pun intended).

Eliz.
 
stapel said:
But the exercise just says "numbers"; it does not specify "whole numbers".
Click to expand...
True, BUT it's highly improbable that it's not whole numbers,
given the fact that poor CMilk has no idea where to start...

Betya a buck 78 is a typo :wink:
 
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