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Question

Given x=a2+b2+a2b2a2+b2a2b2, use componendo and dividendo to prove that a2b2=2a2x2+1.

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Solution

x=a2+b2+a2b2a2+b2a2b2
x=2a2+b22a2b2
a2b2=2a2x2+1
x2=a2+b2a2b2
x2+1=a2+b2+a2b2a2b2

1240494_1137522_ans_b026c5931e574975a88c64f3ed173fdb.jpg

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