Question

IF X=UNDERROOT OF 2+UNDERROOT3 THEN X+1UPON X=?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{x+\frac{1}{x}=2\sqrt{3}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies x = \sqrt{2} + \sqrt{3} \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies x + \frac{1}{x} =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{1}{x} = \frac{1}{ \sqrt{2} + \sqrt{3} } \\ \\ \tt: \implies \frac{1}{x} = \frac{1}{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } \\ \\ \tt: \implies \frac{1}{x} = \frac{ \sqrt{2} - \sqrt{3} }{( \sqrt{2})^{2} - { (\sqrt{3} )}^{2} } \\ \\ \tt: \implies \frac{1}{x} = \frac{ \sqrt{2} - \sqrt{3} }{2 - 3} \\ \\ \tt: \implies \frac{1}{x} = - \sqrt{2} + \sqrt{3} - - - - - (1) \\ \\ \bold{For \: finding \: value : } \\ \tt: \implies x + \frac{1}{x} = \sqrt{2} + \sqrt{3} - \sqrt{2} + \sqrt{3} \\ \\ \green{\tt: \implies x + \frac{1}{x} = 2 \sqrt{3} }$

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{x+\frac{1}{x}=2\sqrt{3}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}}$

$\tt: \implies x = \sqrt{2} + \sqrt{3}$

$\red{\underline \bold{To \: Find :}}$

$\tt: \implies x + \frac{1}{x} =?$

• Given Question

$\bold{As \: we \: know \: that}$

$\tt: \implies \frac{1}{x} = \frac{1}{ \sqrt{2} + \sqrt{3} }$

$\tt: \implies \frac{1}{x} = \frac{1}{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} }$

$\tt: \implies \frac{1}{x} = \frac{ \sqrt{2} - \sqrt{3} }{( \sqrt{2})^{2} - { (\sqrt{3} )}^{2} }$

$\tt: \implies \frac{1}{x} = \frac{ \sqrt{2} - \sqrt{3} }{2 - 3}$

$\tt: \implies \frac{1}{x} = - \sqrt{2} + \sqrt{3} - - - - - (1)$

$\bold{For \: finding \: value : }$

$\tt: \implies x + \frac{1}{x} = \sqrt{2} + \sqrt{3} - \sqrt{2} + \sqrt{3}$

$\green{\tt: \implies x + \frac{1}{x} = 2 \sqrt{3} }$