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Question
If a, b, c and d are in proportion, prove that: (a4 + c4) : (b4 + d4) = a2 c2 : b2 d2.
Solution
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
(a4 + c4) : (b4 + d4) = a2 c2 : b2 d2
L.H.S. = `(a^4 + c^4)/(b^4 + d^4)`
= `(b^4k^4 + d^4k^4)/(b^4 + d^4)`
= `(k^4(b^4 + d^4))/((b^4 + d^4)`
= k4
R.H.S. = `(a^2c^2)/(b^2d^2)`
= `(k^2b^2.k^2d^2)/(b^2.d^2)`
= k4
Hence L.H.S. = R.H.S.
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