Question

If x+1/x=5 then find the value of (x^2+1/x^2) is?

Answer 1

Recall that

$(a+b)^2=a^2+2ab+b^2$

So we have

$\left(x+\dfrac1x\right)^2=x^2+2+\dfrac1{x^2}$

Given that $x+\frac1x=5$, we get

$x^2+\dfrac1{x^2}=5^2-2=\boxed{23}$