If $\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$, then prove that $(a^2+b^2+c^2)(d^2+b^2+c^2)=(ab+bc+cd)^2$

Question

It is given that $\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$.

So how will I prove that $(a^2+b^2+c^2)(d^2+b^2+c^2)=(ab+bc+cd)^2$?

Answer 1

Let $k=\frac{c}{d}$. Then $c=kd,b=k^2d,a=k^3d$. Now simply substitute and simplify.