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Question

If a, b , c, d are positive real numbers such that a2+b2=c2+d2 and a2+d2ad=b2+c2+bc, find the value of ab+cdad+bc

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Solution

a2+b2=c2+d2&a2+d2ad=b2+c2+bc
ab+cdad+bc=?
bc2+d2b2+d2ad=b2+c2+bc
2d2ad=2b2+bc
2d22b2=ad+bc
ad+bc=2cd2b2
similarly
ab+cd=2(a2c2)
ab+cdad+bc=a2c2d2b2

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