Question

28. If x= 2+V3 find the value of x^2+1/x^2​

Answer 1

EXPLANATION.

$\sf : \implies \: x \: = 2 + \sqrt{3} \\ \\ \sf : \implies \: \green{{ \underline{to \: find \: {x}^{2} + \frac{1}{ {x}^{2} } }}}$

$\sf : \implies \: \dfrac{1}{x} = \dfrac{1}{2 + \sqrt{3} } \\ \\ \sf : \implies \: \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \sf : \implies \: \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3}$

$\sf : \implies \: {x}^{2} + \dfrac{1}{ {x}^{2} } = (x + \dfrac{1}{x}) {}^{2} - 2 \: x \: \: \times \dfrac{1}{x} \\ \\ \sf : \implies {x}^{2} + \frac{1}{ {x}^{2} } = (x + \frac{1}{x}) {}^{2} - 2 \\ \\ \sf : \implies \: [(2 + \sqrt{3} ) + (2 - \sqrt{3})] {}^{2} - 2 \\ \\ \sf : \implies \: [ \: 2 + \sqrt{3} + 2 - \sqrt{3} ] {}^{2} - 2 \\ \\ \sf : \implies \: [4] {}^{2} - 2 \\ \\ \sf : \implies \: 16 - 2 = 14$

Answer 2

Answer:

see above................