If $(a+1/a-3)^2=25$then find $a^2+1/a^2$

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(a+1/a-3)^2=25

then find

a^2+1/a^2

A36

B66

C64

D62

Answer:

$(a+1/a-3)^2=25$

$a+1/a-3=\sqrt{25}=5$

$a+1/a-3=5$

$a+1/a=5+3=8$

$a^2+1/a^2=8^2-2$

$=64-2=62$

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

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