Question

Please give as detailed answer as possible for this question. Note: PLEASE DONT SPAM . WINNER WILL GET 20RS PAYTM CASH ADD YOUR UPI ID OR MOBILE NUMBER IN THAT CASE.​

Answer 1

Hey ❤️

here is your answer ⤵️

Answer :

• 9

Solution :

$\longrightarrow$ Here We shall use the identity (a + b)² = a² + b² + 2ab

$\longrightarrow$ So, take here a = x² and b = $\sf \frac{1}{x²}$

Hence,

$\sf \bigg( x² + \frac{1}{x²} \bigg)^{2} = (x²)^{2} + \bigg(\frac{1}{x²} \bigg)^{2} + 2 × (x²)\bigg(\frac{1}{x²} \bigg)$

$\sf \bigg( x² + \frac{1}{x²} \bigg) ^{2} = (x²)^{2} + \bigg(\frac{1}{x²} \bigg)^{2} + 2 × (\cancel{x²})×\bigg(\frac{1}{\cancel{x²}} \bigg)$

$\sf \bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg)^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2$

$\longrightarrow$ Now, According to question, $\sf x^{4} + \frac{1}{x^{4}} = 6239$

$\sf \bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg) ^{2} = 6239 + 2$

$\sf \bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg) ^{2} = 6241$

$\sf {x}^{2} + \frac{1}{ {x}^{2} } = \sqrt{6241}$

$\sf {x}^{2} + \frac{1}{ {x}^{2} } = 79$

$\longrightarrow$ Now, Again We shall use the identity (a + b)² = a² + b² + 2ab

But take here a = x and b = $\sf \frac{1}{x}$

$\sf \bigg( x + \frac{1}{x} \bigg) ^{2} = x² + \bigg(\frac{1}{x}\bigg)^{2} + 2 × (x) × \bigg( \frac{1}{x} \bigg)$

$\sf \bigg( x + \frac{1}{x} \bigg) ^{2} = x² + \bigg(\frac{1}{x}\bigg)^{2} + 2 × \cancel{(x)} × \bigg( \frac{1}{\cancel{x}} \bigg)$

$\sf { \bigg(x + \frac{1}{x} \bigg) }^{2} = {x}^{2} + \frac{1}{x ^{2} } + 2$

$\longrightarrow$ We had already find out that, $\sf x^{2} + \frac{1}{x^{2}} = 79 \: \: So,$

$\sf \bigg(x + \frac{1}{x} \bigg) ^{2} = 79 + 2$

$\sf \bigg(x + \frac{1}{ x} \bigg) ^{2} = 80$

$\sf x + \frac{1}{x} = \sqrt{81}$

$\underline{\boxed{ \sf x + \frac{1}{x} = 9}}$

$\longrightarrow$ Hence, Answer is 9

I hope it helps you ❤️✔️