Question

x/a=y/b=z/c Show that x^3/a^3+y^3/b^3+z^3/c^3=3xyz/abc

Answer 1

let x/a=y/b=z/c=k .then x= ak ,y= bk, z=ck
then the expression on left hand side reduces to
k^3 + k^3+k^3=3k^3
which is equal to expression on the right.
so lhs = rhs

Answer 2

Answer:

Given,

$\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$

Let,

$\frac{x}{a}=\frac{y}{b}=\frac{z}{c}=k$ -------(1)

$(\frac{x}{a})^3+(\frac{y}{b})^3+(\frac{z}{c})^3$

$=k^3+k^3+k^3$

$=3k^3$

$=3(k)(k)(k)$

$=3(\frac{x}{a})(\frac{x}{b})(\frac{x}{c})$ ( From equation (1) )

$=\frac{3xyz}{abc}$

Hence, proved......