Question

If a, b,and c are in G.P. and x, y, respectively, be arithmetic means between a, b and b, c, then the value of $\frac{a}{x}+\frac{c}{y}$is

• A. 1
• B. 2
• C. 1/2
• D. none of these

Answer 1

The correct option is B

2

Given, $b^2=ac$ and $x=\frac{a+b}{2},y=\frac{b+c}{2}$.Therefore,

$\frac{a}{x}+\frac{c}{y}=\frac{2a}{a+b}+\frac{2c}{b+c}$

$=\frac{2a(b+c)+2c(a+b)}{(a+b)(b+c)}$

$=2\frac{2ac+ab+bc}{ab+ac+b^2+bc}$

$=2\frac{2ac+ab+bc}{2ac+ab+bc}$

$=2$