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Question
If `[x, y][(x),(y)] = [25]` and `[(-x, y)][(2x),(y)] = [-2]` find x and y if `x, y ∈ Z` (integer)
Solution
From the question, We have
x2 + y2 = 25 and 2x2 + y2 = −2
x, y ∈ W (integers)
−2x2 + y2 = −2 ⇒ y2 = 2x2 − 2
x2 + y2 = 25
⇒ x2 + 2x2 − 2 = 25
⇒ 3x2 = 27
⇒ x2 = 9
⇒ x = ±3
y2 = 2x2 − 2
y2 = 2 × 32 − 2 = 16
y2 = ±4
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