Question

If $(a+1/a-3)^2=16$ then find $a^2+1/a^2$

• A. 47
• B. 49
• C. 7
• D. 3

Answer 1

Answer:

A. 47

$(a+1/a-3)^2=16$

$a+1/a-3=\sqrt{16}=4$

$a+1/a-3=4$

$a+1/a=4+3=7$

$a^2+1/a^2=7^2-2$

$=49-2=47$

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