Keep it in a proper proportion

Algebra Level 3

If $a,b$ and $c$ are in continued proportion, the expression $\dfrac{a^2+ab+b^2}{b^2+bc+c^2}$ can be simplified into:

\dfrac{c}{a}

\dfrac{a}{c}

\dfrac{a+c}{a+b}

1

2 solutions

Vinayak Srivastava
Jul 31, 2020

$b^2=ac$ $\implies \dfrac{a^2+ab+b^2}{b^2+bc+c^2}=\dfrac{a^2+ab+ac}{ac+bc+c^2}=\dfrac{a(a+b+c)}{c(a+b+c)}=\dfrac{a\cancel{(a+b+c)}}{c\cancel{(a+b+c)}}=\boxed{\dfrac{a}{c}}$

Thomas Athur
Feb 6, 2018

A/b=b/c=k(say) Simplifying the expression we would get the end result as k^2. a=ck^2 So, a/c = k^2 Hence, answer is a/c

Keep it in a proper proportion

2 solutions

0 pending reports