Question

$\text{If a,b, c are in continued proportion,}$
$\text{then the value of}\frac{a^2+ab+b^2}{b^2+bc+c^2}\text{is equal to:}$
[2 marks]

• A. $\frac{a}{c}$
• B. $\frac{a}{b}$
• C. $\frac{b}{a}$
• D. $\frac{c}{a}$

Answer 1

The correct option is A $\frac{a}{c}$

Given,
$a$, $b$, $c$ are in continued proportion.
It means,
$\frac{a}{b}=\frac{b}{c}\therefore b^2=ac$
$\text{Now,}\frac{a^2+ab+b^2}{b^2+bc+c^2}=\frac{a^2+ab+ac}{ac+bc+c^2}=\frac{a(a+b+c)}{c(a+b+c)}=\frac{a}{c}$