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ANSWER THE QUESTION IN THE ATTACHMENT☞NO SPAM❌❌☞NO COPIED ANSWER ❌❌☞BETTER IF EXPLAINED TOO✅​​

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Required answer :-

QUESTION :

•If \: (x + \frac{1}{x}) \: = \: \sqrt{7} \: then \: <klux>FIND</klux> \: the \: values \: of \: {x}^{2} + \frac{1}{x {}^{2} } \: and \: x {}^{4} + \frac{1}{x {}^{4} } \\

Solution :

Given,

•(x + \frac{1}{x}) \: = \: \sqrt{7}

To find,

• values \: of \: {x}^{2} + \frac{1}{x {}^{2} } \: and \: x {}^{4} + \frac{1}{x {}^{4} } \\

Formula used :

•. (a+b)² = a² + b² + 2ab

Step by step explaination : -

According the question we have to square both the terms -

x {}^{2} + \frac{1}{x {}^{2} } \: + \: 2x \: \times \: \frac{1}{x} = 7 \: \\

x {}^{2} + \frac{1}{x {}^{2} } + 2 \: = \: 7 \: \\ x {}^{2} + \frac{1}{x {}^{2} } = 5

Hence, \: <klux>VALUE</klux> \: of \: {x}^{2} + \frac{1}{x {}^{2} } \: is \: 5

Now again we have to square both for calculating the value of SECOND term.

(x {}^{2} + \frac{1}{x {}^{2} } ) {}^{2} = 5

x {}^{4} + \frac{1}{x {}^{4} } + 2x {}^{2} \times \frac{1}{x {}^{2} } = 25

x {}^{4} + \frac{1}{x {}^{4} } + 2 = 25

x {}^{4} + \frac{1}{x {}^{4} } = 23

Hence, \: value \: of \: x {}^{4} + \frac{1}{x {}^{4} } \: is \: 23


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