dont think so hard
x and y are integers where x 2 + y 2 = 1 0 0 0 0 0 . What is the sum of all possible values of x and y?
The answer is 0.
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1 solution
Please update your solution accordingly.
12^2 + 316^2 = 100000
100^2 + 300^2 = 100000
180^2 + 260^2 = 100000
But, why this solution is 0 ?
The 'don't think so hard' reference in the title meant that you can simply divide both sides of the equation by 1 0 0 0 0 = 1 0 0 2 and create additional variables t = 1 0 0 x and z = 1 0 0 y ,. We now have t 2 + z 2 = 1 0 . It's clear that 1 and 9 are the only perfect squares adding up to 1 0 , hence { x = ± 1 0 0 y = ± 3 0 0 or { x = ± 3 0 0 y = ± 1 0 0 .
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U can't get the solution this way.
Even 260²+180²=100000
Its just the ± effect which makes the answer 0
For every positive solution of p and q, there will be a corresponding negative value. All the values will negate and the answer will be 0.