Question

Solve the problem fast ​

Answer 1

$x = 2 + \sqrt{2} \\ {x}^{2} = (2 + \sqrt{2} ) {}^{2} \\ {x}^{2} = {2}^{2} + {( \sqrt{2}) }^{2} + 2 \times 2 \times \sqrt{2} \\ {x}^{2} = 4 + 2 + 4 \sqrt{2} = 6 + 4 \sqrt{2} \\ \\ \frac{1}{ x } = \frac{1}{2 + \sqrt{2} } = \frac{2 - \sqrt{2} }{4 - 2} = \frac{2 - \sqrt{2} }{2} \\ \frac{1}{ {x}^{2} } = {( \frac{2 - \sqrt{2} }{2} )}^{2} = \frac{4 + 2 - 4 \sqrt{2} }{4} \\ \: \: \: \: \: \: \: = \frac{6 - \sqrt{2} }{4}$

$\frac{4}{ {x}^{2} } = 4 \times \frac{1}{ {x}^{2} } = \frac{4(6 - 4 \sqrt{2}) }{4} = 6 - 4 \sqrt{2}$

Therefore,

${x}^{2} + \frac{4}{ {x}^{2} } = 6 + 4 \sqrt{2} + 6 - 4 \sqrt{2} = 12$

Therefore, the final answer is 12

Hope this is helpful to you

Pls mark as brainliest

Follow me and I'll follow you back

Answer 2

Answer:

Step-by-step explanation:

x^2=(2+$\sqrt{2)$)^2=6+4$\sqrt{2}$

x^2+4/x^2=6+4$\sqrt{2}$+4/6+4$\sqrt{2}$=

6+4$\sqrt{2}$+  4/6+4$\sqrt{2}$*6-4$\sqrt{2}$/6-4$\sqrt{2}$=6+4$\sqrt{2}$+24-16$\sqrt{2}$/4

=(6+4$\sqrt{2}$)4/4+24-16$\sqrt{2}$/4=24 + 16$\sqrt{2}$+24-16$\sqrt{2}$/4=48/4=12