If a+1/a = 12, then find the value of a2+1/a2 - SSC STUDY

If $a+ \frac1a$ = 12, then find the value of $a^2+ \frac{1}{a^2}$

Options
a) 142
b) 140
c) 146
d) 144

Solution

As per question
$a+ \frac1a$ = 12
Square both side
$(a+ \frac1a)^2$ = (12)²
$a^2+ \frac{1}{a^2}+ 2 \times a \times \frac1a$ = 144
$a^2+ \frac{1}{a^2}+2$ = 144
$a^2+ \frac{1}{a^2}$ = 144 – 2
$a^2+ \frac{1}{a^2}$ = 142

Answer: 142