Question

if (x-1/x) =7 , then find the value of (x²+1/x²)​

Answer 1

SOLUTION:-

$x - \frac{1}{x} = 7 \\ \\ {(x - \frac{1}{x}) }^{2} = {7}^{2} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 \times x \times \frac{1}{x} = 49 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 49 +2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 51$

ANSWER=51

Answer 2

$\large{\mathfrak{\underline{\underline{Answer :-}}}}$

51 Answer

Given :-

${ \bf{x - \frac{1}{x} = 7}}$

✯ Let this equation be equation 1.

To Find :-

$\large{ \bf {x}^{2} + \frac{1}{ {x}^{2} }}$

Solution :-

_______________[Using equation 1]

✯ Squaring both side

$\large{\bf{(x \: - \: {\frac{1}{x}})^{2} \: = \: 7^{2}}}$

✯ Using Identity :-

$\huge{\sf{\boxed{\boxed{(a - b) ^{2} = a^{2} + b^{2} - 2(a)(b)}}}}$

$\large{\sf{{x}^{2} + \frac{1}{ {x}^{2} } \: \: - 2 \times x \times \frac{1}{x} = \: {7}^{2}}}$

$\large{\sf{{x}^{2} \: + \frac{1}{{x}^{2}} - 2 \times \cancel{x} \times \cancel\frac{1}{x} \: = \: 49}}$

$\large{\sf{{x}^{2} + \frac{1}{{x}^{2}} = \: 49 \: + \: 2}}$

$\large{\sf{{x}^{2} + \frac{1}{{x}^{2}} = 51}}$

${\bf{\huge{\boxed{{x}^{2} + \frac{1}{ {x}^{2}} = \: {\boxed{51}}}}}}$