Question

x= root[ 3+2 root2] then find the value of x to the power 4 +1/x to the power4

Answer 1

HELLO DEAR,

$\sf{GIVEN:-}$ $\mathit{x = \sqrt{(3 + 2\sqrt{2})}}$

$\mathit{x^2 = (3 + 2\sqrt{2})}$

$\mathit{x^4 = (3 + 2\sqrt{2})^2}\\ \\ \mathit{x^4 = (9 + 8 + 12\sqrt{2})}$--------------( 1 )

1/x⁴ = 1/(17 + 12√2) * (17 - 12√2)/(17 - 12√2)

1/x⁴ = (17 - 12√2)/(289 - 288)

1/x⁴ = (17 - 12√2)---------------( 2 )

adding-----------( 1 ) & -----------( 2 )

x⁴ + 1/x⁴ = (17 + 12√2) + (17 - 12√2)

x⁴ + 1/x⁴ = (17 + 17 + 12√2 - 12√2)

x⁴ + 1/x⁴ = 34