Question

hey mates

please help me it is very very urgent​

Answer 1

Answer:

(√5+2)^2+1

(√5+2)^2

5+4+4√5+1

5+4+4√5

9+4√5+1

9+4√5

Answer 2

ANSWER:-

Given:

x=√5+2.

To find:

Find the value of x² + 1/x².

Solution:

${x}^{2} = ( \sqrt{5} + 2) {}^{2} \\ \\ = > ( \sqrt{5} ) {}^{2} + {(2)}^{2} + 2 \times \sqrt{5} \times 2 \\ \\ = > 5 + 4 + 4 \sqrt{5} \\ \\ = > 9 + 4 \sqrt{5}$

$\frac{1}{ {x}^{2} } = \frac{1}{9 + 4 \sqrt{5} } \times \frac{9 - 4 \sqrt{5} }{9 - 4 \sqrt{5} } \\ \\ = > \frac{9 - 4 \sqrt{5} }{( {9)}^{2} - ( {4 \sqrt{5} )}^{2} } \\ \\ = > \frac{9 - 4 \sqrt{5} }{81 - 16 \times 5} \\ \\ = > \frac{9 - 4 \sqrt{5} }{81 - 80} \\ \\ = > \frac{9 - 4 \sqrt{5} }{1} \\ \\ = > 9 - 4 \sqrt{5} \\ Now ,\\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 9 + 4 \sqrt{5} + 9 - 4 \sqrt{5} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 9 + 9 \\ \\ = > 18$

Hope it helps ☺️