Question 1207444: Write down the integral solutions of the form (𝒙, 𝒚) satisfying the relation 𝒙𝟐 + 𝒚𝟐 = 𝟏𝟐𝟏
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
I'll assume the equation is x^2+y^2 = 121
The two integer solutions are
(0,11) and (11,0)
This is something found by guess-and-check, or simply note that 121 is a perfect square.
11^2 = 11*11 = 121
Also notice how if x = 1, then it leads to y^2 = 120, but 120 isn't a perfect square.
This would therefore lead to y not being an integer.
This rules out x = 1 being a possibility.
If x = 2, then it leads to y^2 = 117 which also isn't a perfect square.
And so on.
Follow this logic for other x values to find that only 0 and 11 work.
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