Question

If the $a+\frac{4}{a}=4$, then what is the value of $a^4+\frac{1}{a^2}$?

• A. 16.25

Answer 1

The correct option is A 16.25
Given,
$a+\frac{4}{a}=4$
$\frac{a^2+4}{a}=4$
$a^2+4-4a=0$
$(a-2{)}^2=0$
$a=2$

$\therefore a^4=16and{a}^2=4$
The value of $16+\frac{1}{4}=16+0.25=16.25$