Question

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

Answer 1

`(x-1)/(x)=8\\\\(x)/(x)-(1)/(x)=8\\\\1-(1)/(x)=8\ \ \ \ |-1\\\\-(1)/(x)=7\ \ \ \ |\cdot(-1)\\\\(1)/(x)=-7\ \ \ \ \ |^2\\\\(1^2)/(x^2)=(-7)^2\\\\(1)/(x^2)=49\qquad(*)`

-------------------------------------------------------------

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

`Answer:\ (x^2+1)/(x^2)=50`