Question

If $\frac{1}{b+c},\frac{1}{c+a},\frac{1}{a+b}$ are in AP, then $a^2,b^2,c^2$ will be in.

• A. AP
• B. GP
• C. HP
• D. None of these

Answer 1

The correct option is A AP

Given $\frac{1}{b+c},\frac{1}{c+a},\frac{1}{a+b}$ are in A.P
$\Rightarrow \frac{1}{c+a}-\frac{1}{b+c}=\frac{1}{a+b}-\frac{1}{c+a}$
$\Rightarrow \frac{b-a}{b+c}=\frac{c-b}{a+b}$
$\Rightarrow b^2-a^2=c^2-b^2\Rightarrow 2b^2=a^2+c^2$
Therefore, $a^2,b^2,c^2$ are in A.P
Hence, option 'A' is correct.