If $x+1/x=sqrt5$ , find the value of $x^2+1/x^2$ ?

Mar 8, 2017

$3$

We square both sides.

$(x + 1/x)^2 = sqrt(5)^2$

$x^2 + 2 + 1/x^2 = 5$

$x^2 + 1/x^2 = 3$

Hopefully this helps!

Mar 8, 2017

$x+ 1/x = sqrt(5) -> (x+1/x)^2 = sqrt(5)^2$
$x^2+(2 * x * 1/x) + (1/x)^2 = 5$
$x^2+2x/x+1/x^2 = 5$
$x^2+2+1/x^2=5$
$x^2+1/x^2 = 5-2 = 3$

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If x+1/x=sqrt5x+1/x=sqrt5, find the value of x^2+1/x^2x^2+1/x^2?