Question

if x = 2 + √3 find the value of x ka square 2 +1 by x ka square

Answer 1

hi friend!

Here is your Answer

Given that

X = 2+ √3

then
$\frac{1}{x} = \frac{1}{2 + \sqrt{3} } \\ by \: rationalising \\ \\ = \: \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ = \frac{2 - \sqrt{3} }{ {2}^{2} - { \sqrt{3} }^{2} } = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ = 2 - \sqrt{3} \\ \\ now \\ \\ (x + \frac{1}{ {}^{x} } ) {}^{2} = {x }^{2} + \frac{1}{ {x}^{2} } + 2x \times \frac{1}{x} \\ \\ (2 + \sqrt{3 } + 2 - \sqrt{3} {)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ (4 {)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 14 \: ans$

Answer 2

Solution:-


i will be edit ................