Question

if x is equals to 3 + 2 root 2 find the value of x raise to power 4 + 1 upon X raise to power 4

Answer 1

(x+1/x)^2=x^2+1/x^2+2 as 2*1/x*x=2
And Same will happen with (x^2+1/x^2)^2

Answer 2

Answer:

Value of given expression is 1154.

Step-by-step explanation:

Given: x = 3 + 2√2

To find: $x^4+\frac{1}{x^4}$

Consider,

x² = ( 3 + 2√2 )² = 3² + (2√2)² + 2(3)(2√2) = 9 + 8 + 12√2 = 17 + 12√2

$x^4=(17+12\sqrt{2})^2=17^2+(12\sqrt{2})^2+2(17)(12\sqrt{2})=289+288+408\sqrt{2}=577+408\sqrt{2}$

$\frac{1}{x^4}=\frac{1}{577+408\sqrt{2}}=\frac{1}{577+408\sqrt{2}}\times\frac{577-408\sqrt{2}}{577-408\sqrt{2}}=\frac{577-408\sqrt{2}}{(577)^2-(408\sqrt{2})^2}=\frac{577-408\sqrt{2}}{332929-332928}=577-408\sqrt{2}$

So,  $x^4+\frac{1}{x^4}=577+408\sqrt{2}+577-408\sqrt{2}=577+577=1154$

Therefore, Value of given expression is 1154.