#### Question

If y is the mean proportional between x and z, show that :

xyz (x+y+z)^{3} =(xy+yz+xz)^{3}

#### Solution

Since y is the mean proportion between x and z

y^{2} = xz

LHS

xyz (x + y + z)^{3}

= yy^{2} (x + y + z)^{3}

= y^{3} (x + y +z)^{3}

= [y (x + y + z)]^{3}

= (xy + y^{2} + yz)^{3}

= (xy + y^{2} + yz)^{3} = RHS

LHS = RHS

Is there an error in this question or solution?

Solution If Y is the Mean Proportional Between X and Z, Show that : Concept: Proportions.