Question

Find the value of.
${\left(\frac{1}{2}\right)}^{-2}+{\left(\frac{1}{3}\right)}^{-2}+{\left(\frac{1}{4}\right)}^{-2}$

Answer 1

We have,

${\left(\frac{1}{2}\right)}^{-2}+{\left(\frac{1}{3}\right)}^{-2}+{\left(\frac{1}{4}\right)}^{-2}$

$=(2{)}^2+{\left(3\right)}^2+{\left(4\right)}^2$ [Using the identity $a^{-1}=\frac{1}{a}$]

$=4+9+16$

$=29$