Question

if x^2-5x-1=0 then find the value of x^2+1/x2

Answer 1

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Answer 2

x^2+1/x2 = 23

Step-by-step explanation:

Given:

We have,

$x^2-5x+1=0$

$x^2+1=5x$

Dividing both the sides by x, we get

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

$x+\frac{1}{x} =5$                    [1]

Now, $x^2+\frac{1}{x^2}$

⇒ $x^2+\frac{1}{x^2}+ 2 -2$

⇒ $x^2+2+\frac{1}{x^2} -2$

⇒ $(x+\frac{1}{x} )^2-2$                 [$(x+\frac{1}{x} )^2=x^2+2\times x\times \frac{1}{x} +\frac{1}{x^2}$]

⇒ $(5)^2-2$

⇒ 25 - 2                                             [from 1]

⇒ 23

Hence $x^2+\frac{1}{x^2}$ = 23