Question

$\tt If \: \: \dfrac{1}{a+1} + \dfrac{1}{b+1} + \dfrac{1}{c + 1} = 2$
$\tt then, \: \: a^2 + b^2 + c^2 = ?$ ​

Answer 1

Given:-

$\sf \large If \: \: \dfrac{1}{a+1} + \dfrac{1}{b+1} + \dfrac{1}{c + 1} = 2$

To Find:-

$\sf \large a { }^{2} + b {}^{2} + c {}^{2} = ?$

Solution:-

This is a cyclic function. This will held when a = b = c.

$\sf \large So, ⇒ \frac{3}{1 + a} = 2.$

$\sf \large ⇒a = b = c = \frac{1}{2}$

$\sf \large Hence, a {}^{2} + b {}^{2} + c {}^{2} =( \frac{1}{2} ) {}^{2} + ( \frac{1}{2} ) {}^{2} + ( \frac{1}{2} ) {}^{2} = \frac{3}{4}$

Answer:-

$\sf \large \red{ a {}^{2} + b {}^{2} + c {}^{2} = \frac{3}{4} .}$

Hope you have satisfied. ⚘