If $(a+1/a-3)^2=49$then find $a^2+1/a^2$

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If $(a+1/a-3)^2=49$ then find $a^2+1/a^2$

A100

B99

C98

D97

Answer:

$(a+1/a-3)^2=49$

$a+1/a-3=\sqrt{49}=7$

$a+1/a-3=7$

$a+1/a=7+3=10$

$a^2+1/a^2=10^2-2$

$=100-2=98$

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

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