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Question
If (a2 + b2)(x2 + y2) = (ax + by)2; prove that: `a/x = b/y`.
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Solution
Given that, (a2 + b2)(x2 + y2) = (ax + by)2
a2x2 + a2y2 + b2x2 + b2y2 = a2x2 + b2y2 + 2abxy
a2y2 + b2x2 – 2abxy = 0
(ay – bx)2 = 0
ay – bx = 0
ay = bx
`a/x = b/y`
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