Question

If $a,b,c$ are in continued proportion, then prove that $\frac{a}{a+2b}=\frac{a-2b}{a-4c}$

Answer 1

Given that $a,b,c$ are in continued proportion.

$\therefore b^2=ac$

To prove:- $\frac{a}{a+2b}=\frac{a-2b}{a-4c}$

Proof:-

$\frac{a}{a+2b}=\frac{a-2b}{a-4c}$

$a(a-4c)=(a-2b)(a+2b)$

$a^2-4ac=a^2-4b^2$

$4ac=4ac(\because b^2=ac)$

$\Rightarrow 0=0$

L.H.S. $=$ R.H.S.

Hence proved.