If $(a+1/a-3)^2=36$then find $a^2+1/a^2$

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If $(a+1/a-3)^2=36$ then find $a^2+1/a^2$

A82

B83

C81

D79

Answer:

$(a+1/a-3)^2=36$

$a+1/a-3=\sqrt{36}=6$

$a+1/a-3=6$

$a+1/a=6+3=9$

$a^2+1/a^2=9^2-2$

$=81-2=79$

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

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