Question

if x=1+root2 find the value X2+1/x2

Answer 1

Hi ...dear...here is your answer....

Answer 2

Answer:

Value of $x^2+\frac{1}{x^2}$ is 6.

Step-by-step explanation:

Given: $x=1+\sqrt{2}$

To find: $x^2+\frac{1}{x^2}$

x² = ( 1 + √2 )² = 1² + (√2)² + 2 × 1 × √2 = 1 + 2 + 2√2 = 3 + 2√2

$\frac{1}{x^2}=\frac{1}{3+2\sqrt{2}}=\frac{1}{3+2\sqrt{2}}\times\frac{3-2\sqrt{2}}{3-2\sqrt{2}}$

                        $=\frac{3-2\sqrt{2}}{3^2-(2\sqrt{2})^2}=\frac{3-2\sqrt{2}}{9-8}=3-2\sqrt{2}$

Now,

$x^2+\frac{1}{x^2}=3+2\sqrt{2}+3-2\sqrt{2}=6$

Therefore, Value of $x^2+\frac{1}{x^2}$ is 6