Question

if x²+1/x²=3find the value of x + 1/x​

Answer 1

Given :

$\large\sf {x}^{2} + \dfrac{1}{ {x}^{2} } = 3$

To find :

$\large\sf {x} + \dfrac{1}{ {x} }$

Formula used :

$\bf {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

Solution :

$\implies\sf {x}^{2} + \dfrac{1}{ {x}^{2} } = 3$

We know :-

$\sf{({x} + \dfrac{1}{ {x} } )}^{2} = {x}^{2} + {(\dfrac{1}{ {x} })}^{2} + 2 \times (x )\times (\dfrac{1}{ {x} })$

$\implies\sf{({x} + \dfrac{1}{ {x} } )}^{2} = {x}^{2} + {\dfrac{1}{ {x}^{2} }} + 2$

$\implies\sf{({x} + \dfrac{1}{ {x} } )}^{2} = 3 + 2$

$\implies\sf{({x} + \dfrac{1}{ {x} } )}^{2} = 5$

$\implies\sf{{x} + \dfrac{1}{ {x} } } = \sqrt{5}$

Answer :

$\sqrt{5}$

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$\large\bf\blue{Additional-Information}$

$\implies{(a+b)^2 = a^2 + b^2 + 2ab}$

$\implies{(a-b)^2 = a^2 + b^2 - 2ab}$

$\implies{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\implies{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\implies{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$