Question

if x=√5+2,then find the value of x²+1/x²​.
HI DEAR
MY EXAMS IS ALSO GOING GOOD
( ◜‿◝ )​

Answer 1

[tex]\mathfrak{ \huge{Answer:-} } \\ x = \sqrt{5} + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ = {( \sqrt{5} + 2) }^{2} + \frac{1}{ {( \sqrt{5} + 2) }^{2} } \\ = 5 + 4 + 4 \sqrt{5} + \frac{1}{5 + 4 + 4 \sqrt{5} } \\ = 9 + 4 \sqrt{5} + \frac{1}{9 + 4 \sqrt{5} } \\ = \frac{ {(9 + 4 \sqrt{5} )}^{2} + 1}{9 + 4 \sqrt{5} } \\ = \frac{81 + 80 + 72 \sqrt{5} + 1}{9 + 4 \sqrt{5} } \\ = \frac{162 + 72 \sqrt{5} }{9 + 4 \sqrt{5} } \\ = \frac{18(9 + 4 \sqrt{5} )}{(9 + 4 \sqrt{5} )} \\ = 18\\\boxed{ \large{\sf{ {x}^{2}+\frac{1}{{x}^{2} } = 18}} } [/tex]