Question

x + 1/x = 7 x-1/x = 5 find = x² - 1/x²​

Answer 1

Step-by-step explanation:

Given that:

$\tt \pink{x + \frac{1}{x} = 7 \: , \: x - \frac{1}{x} = 5}$

To find:

$\tt{The \: value \: of \: \green{{x}^{2} - \frac{1}{ {x}^{2} } } }\: in \: both \: cases$

Solution:

We have,

$\tt \pink{x + \frac{1}{x} = 7}$

Squaring on both sides, we get

$\tt \pink {{(x} + \frac{1}{ {x}}) ^{2} } = {7}^{2}$

Using algebraic Identity:

$\tt(x + y {)}^{2} = (x + y)(x + y) = \red{{x}^{2} + 2xy + {y}^{2}} ,We \: get$

•––––––☆––––––•

Now,

$\tt \pink {{(x} + \frac{1}{ {x} } ) ^{2} } = 7^{2}$

$⟹ \tt \pink{{x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} } = 49$

$⟹ \tt \pink{{x}^{2} + \frac{1}{ {x}^{2} } + 2 \times \cancel x \times \frac{1}{ \cancel x} } = 49$

$⟹ \tt \pink{{x}^{2} + \frac{1}{ {x}^{2} }} = 49 - 2$

$⟹ \tt \pink{{x}^{2} + \frac{1}{ {x}^{2} }} = 47$

Sorry your question is not correct.