Question

if x-1/x =8, find the value of x^2+1/x^2

Answer 1

$\dfrac{x-1}{x}=8\\\\\dfrac{x}{x}-\dfrac{1}{x}=8\\\\1-\dfrac{1}{x}=8\ \ \ \ |-1\\\\-\dfrac{1}{x}=7\ \ \ \ |\cdot(-1)\\\\\dfrac{1}{x}=-7\ \ \ \ \ |^2\\\\\dfrac{1^2}{x^2}=(-7)^2\\\\\dfrac{1}{x^2}=49\qquad(*)$

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$\dfrac{x^2+1}{x^2}=\dfrac{x^2}{x^2}+\dfrac{1}{x^2}=1+\underbrace{\boxed{\dfrac{1}{x^2}}}_{(*)}=1+48=50$

$Answer:\ \dfrac{x^2+1}{x^2}=50$