Answer:
18
Step-by-step explanation:
If we plug (√5+2) into the equation x^2 + 1/x^2, you will get:
(√5+2)^2 + 1/(√5+2)^2
Then just plug it into a calculator and you're golden.
[tex]\huge\fbox{Answer ☘}[/tex]
x = √5 + 2
[tex]x {}^{2} + \frac{1}{ x {}^{2} } = ?\\ \\( \sqrt{5} + 2) {}^{2} + \frac{1}{( \sqrt{5} + 2) {}^{2} } \\\\ = > (5 + 4 \sqrt{5} + 4) + ( \frac{1}{5 + 4 \sqrt{5} + 4}) \\\\ = > (4 \sqrt{5} + 9) + ( \frac{1}{4 \sqrt{5} + 9 } ) \\ \\ = > \frac{(4 \sqrt{5 } + 9) {}^{2} +1 }{4 \sqrt{5} + 9} \\\\ = > \frac{80 + 81 + 72 \sqrt{5} + 1}{4 \sqrt{5} + 9} \\\\ = > \frac{162 + 72 \sqrt{5} }{4 \sqrt{5} + 9} \\ \\= > \frac{16 + 72 \sqrt{5} }{4 \sqrt{5} + 9} \times \frac{4 \sqrt{5} - 9}{4 \sqrt{5} - 9} \\\\ = > \frac{64 \sqrt{5 } - 144 + 1440 - 648 \sqrt{5} }{80 - 81} \\ \\ = > \frac{1296 - 584 \sqrt{5} }{ - 1} \\\\\bold\pink{ = > 584 \sqrt{5} - 1296}[/tex]
hope helpful~
