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Question
If y is mean proportional between x and z, prove that xyz (x + y + z)³ = (xy + yz + zx)³.
Solution
∵ y is the mean proportional between x and z, then
y2 = xz …(i)
L.H.S. = xyz (x + y + z)3
= xzy (x + y+ z)3
= y2 y(x + y+ z)3 ...[from (i)]
= [y (x + y + z)]3
= [xy + y2 + yz]3 ...[from (i)]
= (xy + xz + yz)3
= (xy + yz + zx)3
= R.H.S.
∵ L.H.S = R.H.S. hence proved.
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