If $x + \frac{1}{x} = \sqrt{5}$ $x+1/x=sqrt5$ , find the value of $x^{2} + \frac{1}{x^{2}}$ $x^2+1/x^2$ ?

Question

If $x + \frac{1}{x} = \sqrt{5}$ $x+1/x=sqrt5$ , find the value of $x^{2} + \frac{1}{x^{2}}$ $x^2+1/x^2$ ?

2 Answers

Impact of this question

4466 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-08T02:34:48

$3$ $3$

Explanation:

We square both sides.

${(x + \frac{1}{x})}^{2} = {\sqrt{5}}^{2}$ $(x + 1/x)^2 = sqrt(5)^2$

$x^{2} + 2 + \frac{1}{x^{2}} = 5$ $x^2 + 2 + 1/x^2 = 5$

$x^{2} + \frac{1}{x^{2}} = 3$ $x^2 + 1/x^2 = 3$

Hopefully this helps!

Answer 2 · 2017-03-08T14:10:51

3

Explanation:

$x + \frac{1}{x} = \sqrt{5} \to {(x + \frac{1}{x})}^{2} = {\sqrt{5}}^{2}$ $x+ 1/x = sqrt(5) -> (x+1/x)^2 = sqrt(5)^2$
$x^{2} + (2 \cdot x \cdot \frac{1}{x}) + {(\frac{1}{x})}^{2} = 5$ $x^2+(2 * x * 1/x) + (1/x)^2 = 5$
$x^{2} + 2 \frac{x}{x} + \frac{1}{x^{2}} = 5$ $x^2+2x/x+1/x^2 = 5$
$x^{2} + 2 + \frac{1}{x^{2}} = 5$ $x^2+2+1/x^2=5$
$x^{2} + \frac{1}{x^{2}} = 5 - 2 = 3$ $x^2+1/x^2 = 5-2 = 3$

Science

Math

Humanities

... and beyond

If $x + \frac{1}{x} = \sqrt{5}$ $x+1/x=sqrt5$ , find the value of $x^{2} + \frac{1}{x^{2}}$ $x^2+1/x^2$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

If x+1x=√5x+1/x=sqrt5, find the value of x2+1x2x^2+1/x^2?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

If $x + \frac{1}{x} = \sqrt{5}$ $x+1/x=sqrt5$ , find the value of $x^{2} + \frac{1}{x^{2}}$ $x^2+1/x^2$ ?