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Question
If y is the mean proportional between x and z, show that :
xyz (x+y+z)3 =(xy+yz+xz)3
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Solution
Since y is the mean proportion between x and z
y2 = xz
LHS
xyz (x + y + z)3
= yy2 (x + y + z)3
= y3 (x + y +z)3
= [y (x + y + z)]3
= (xy + y2 + yz)3
= (xy + y2 + yz)3 = RHS
LHS = RHS
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