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+\frac1x\right)^2=x^2+2+\frac1{x^2}`

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

`x^2+\frac1{x^2}=5^2-2=\boxed{23}`