Question

x+1/x=3 then x2+1/x2=???​

Answer 1

Answer:

Step-by-step explanation:

Just apply squares to both sides of the first expression

$x+\dfrac{1}{x}=3 \Longrightarrow \left(x+\dfrac{1}{x}\right)^2=9$

Since

$\left(x+\dfrac{1}{x}\right)^2=x^2+2x\cdot\dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=x^2+2+\dfrac{1}{x^2}$

Then

$x^2+2+\dfrac{1}{x^2}=9\Longrightarrow x^2+\dfrac{1}{x^2}=7$