Question

If $(a+1/a-3)^2=81$then find $a^2+1/a^2$

• A. 148
• B. 146
• C. 142
• D. 144

Answer 1

Answer:

C. 142

$(a+1/a-3)^2=81$

$a+1/a-3=\sqrt{81}=9$

$a+1/a-3=9$

$a+1/a=9+3=12$

$a^2+1/a^2=12^2-2$

$=144-2=142$

if $a+1/a=k$ then $a^2+1/a^2=k^2-2$