Question

if x = 3+
√8
Find value of x1/x; x⁴1/ x4​

Answer 1

Answer:

1154

Step-by-step explanation:

If x = 3 + $\sqrt{8}$

x = 3 + 2$\sqrt{2}$.

x^2 = 9 + 8 + 12$\sqrt{2}$  = 17 + 12$\sqrt{2}$

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

= 577 + 408$\sqrt{2}$

Thus x^4 + 1/x^4

= 577 + 408$\sqrt{2}$ + 1/(577+408$\sqrt{2}$)

Rationalize it by multiplying the terms with $\frac{577 - 408\sqrt{2} }{577 - 408\sqrt{2} }$

Simplify and answer is 1154

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