Question

if x=√5+2 find value of x^2+1/x^2​

Answer 1

Answer:

1⅐ or 50/7

Step-by-step explanation:

x² + 1/x²

(✓5+2)² + 1/(✓5+2)²

5 + 2 + 1/5+2

7 + 1/7

= 1⅐ or 50/7

Answer 2

$\huge \sf \color{red}\underline{Answer :}$

18

$\huge \sf \color{red}\underline{Solution :}$

Put the value of x in $\large\color{blue} \ \ \ \sf x²+\frac{1}{x²}$

Firstly , we will find value of x²

so,

(√5+2)²

=> 5+4+4√5

=> 9+4√5

Now, we will find value of $\sf \large \frac{1}{x²}$

$\frac{1}{(√5+2)²} \\ \\ \frac{1}{9+4√5} \\ \\ \large \sf Rationalising \\ \\ \frac{1}{9+4√5}×\frac{9-4√5}{9-4√5} \\ \\ \frac{9+4√5}{81-90} \\ \\ \frac{9+4√5}{-9}$

Now we will add x²+1/x²

$9+4√5 + \large \frac{9+4√5}{-9}$

By solving , you will get 18

$━━━━━━━━━━━━━━━━━━━━━━━━━$