Question

if a:b=c:d,prove that (a2+c2) (b2+d2(=(ab+cd(2

Answer 1

Given a:b=c:d
==>. a÷b. = c÷d
==>. ad=bc
Now (a^2 + c^2)(b^2+d^2). = a^2b^2 + a^2d^2 + b^2c^2 + c^2d^2
==> a^2b^2 + b^2c^2 + b^2c^2 + c^2d^2
==> a^2b^2 + 2 b^2c^2 + c^2d^2
==> a^2b^2 + 2 bcad + c^2d^2
==>(ab+cd)^2

Hope you understand
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