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