Question

If $x^2-3x+1=0$ then find the value of $x^2+\frac{1}{x^2}$.

Answer 1

Given, $x^2-3x+1=0$

or, $x^2+1=3x$

or, $x+\frac{1}{x}=3$

Now square both sides we get,

$x^2+2+\frac{1}{x^2}=9$

or, $x^2+\frac{1}{x^2}=9-2$

or, $x^2+\frac{1}{x^2}=7$.