Question

(14) If X=3+V8,,Find the value of X2-1/X2​

Answer 1

Answer : 33.88

I hope it will help you

Answer 2

12√8.

Step-by-step explanation:

Given :

$x = 3 + \sqrt{8}$

To find :

The value of ;

${x}^{2} - \frac{1}{ {x}^{2} }$

Solution :

$\frac{1}{x} = \frac{1}{(3 + \sqrt{8} )} \\ \implies \: \frac{1}{x} = \frac{1 \times (3 - \sqrt{8} )}{(3 + \sqrt{8} ) \times (3 - \sqrt{8} )} \\ \implies \: \frac{1}{x} = \frac{3 - \sqrt{8} }{ {3}^{2} - {( \sqrt{8} )}^{2} } \\ \implies \: \frac{1}{x} = \frac{3 - \sqrt{8} }{9 - 8} = 3 - \sqrt{8}$

Now,

$x + \frac{1}{x} = 3 + \sqrt{8} + 3 - \sqrt{8} = 6$

And,

$x - \frac{1}{x} = 3 + \sqrt{8} - 3 + \sqrt{8} = 2 \sqrt{8}$

Now,

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

Therefore,

${x}^{2} - \frac{1}{ {x}^{2} } = 6 \times 2 \sqrt{8} = 12 \sqrt{8}$

Hence, the answer is = 12√8.