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(a-b)^2 Expansion and Visualisation

If x2+y2=57 a...

Question

If $x^{2} + y^{2} = 57$ and xy = 16 and x is bigger than y .find (x-y)?

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Solution

$x^{2} + y^{2} = 57 x y = 16 (x + y)^{2} - 21 x y = (x - y)^{2} x^{2} + y^{2} + 2 x y - 4 x y = (x - y)^{2} 57 - 2 \times 16 = (x - y) 57 - 32 25 = (x - y)^{2} 5 = x - y$

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