Question

If x + 1/x = 5, then value of x^2 + 1⁄x^2



25

10

23

27

​

Answer 1

Solution:-

Given:-

$: \implies \rm \: x + \dfrac{1}{x} = 5$

To find :-

$: \implies \rm \: {x}^{2} + \dfrac{1}{ {x}^{2} }$

Now take

$: \implies \rm \: x + \dfrac{1}{x} = 5$

:- squaring on both side

$: \implies\rm \: \bigg(x + \dfrac{1}{x} \bigg)^{2} = {5}^{2}$

Using this identities:- ( a + b )² = a² + b² + 2ab , we get

$: \implies \rm {x}^{2} + \dfrac{1}{ {x}^{2} } + 2 \times x \times \dfrac{1}{x} = 25$

$: \implies \rm {x}^{2} + \dfrac{1}{ {x}^{2} } + 2 \times \not{x} \times \dfrac{1}{ \not{x}} = 25$

$\rm : \implies \: {x}^{2} + \dfrac{1}{x {}^{2} } + 2 = 25$

$\rm : \implies {x}^{2} + \dfrac{1}{ {x}^{2} } = 25 - 2$

$\rm : \implies {x}^{2} + \dfrac{1}{ {x}^{2} } = 23$

$\underline{\rm \: so \: value \: of \: \rm \: {x}^{2} + \dfrac{1}{ {x}^{2} } \: is \: 23}$