Question

(x^2+1/x^2)=38,find the value of x+1/x

Answer 1

We have

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

and given that

`x^2+\frac1{x^2}=38`

it follows that

`\left(x+\frac1x\right)^2=40\implies x+\frac1x=\pm√(40)`