Question

×^2+1/×^2=27 find the value of ×+1/×​

Answer 1

${x}^{2} \: + \: \dfrac{1}{{x}^{2}} \: = \: 27$

__________ [GIVEN EQUATION]

• We have to find the value of $x \: + \: \dfrac{1}{x}$

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${x}^{2} \: + \: \dfrac{1}{{x}^{2}} \: = \: 27$

We know that..

a² + b² = (a + b)² - 2ab

$\implies$ ${ \bigg(x \: + \: \dfrac{1}{x} \bigg)}^{2}$ - $2{ \cancel{x}} \: \times \: \dfrac{1}{ \cancel{x}}\:=\:27$

$\implies$ ${ \bigg(x \: + \: \dfrac{1}{x} \bigg)}^{2}$ - $2\:=\:27$

$\implies$ ${ \bigg(x \: + \: \dfrac{1}{x} \bigg)}^{2}$ = $27\:+\:2$

$\implies$ ${ \bigg(x \: + \: \dfrac{1}{x} \bigg)}^{2}$ = $29$

$\implies$ $x \: + \: \dfrac{1}{x}$ = $\sqrt{29}$

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$\implies$ $x \: + \: \dfrac{1}{x}$ = $\sqrt{29}$

___________ [ANSWER]

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