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Question: If x = 3 – \(\sqrt{8}\), then x<sup>3</sup> + \(\frac{1}{x^{3}}\) is equal to –...

If x = 3 – 8\sqrt{8}, then x3 + 1x3\frac{1}{x^{3}} is equal to –

A

6

B

198

C

6 2\sqrt{2}

D

102

Answer

198

Explanation

Solution

x3 +1x3\frac{1}{x^{3}}= (3–8)3+1(3–8)3(3–\sqrt{8})^{3} + \frac{1}{(3–\sqrt{8})^{3}}

= (3–8)3(3–\sqrt{8})^{3}+ (3+8)3(3 + \sqrt{8})^{3}

= 2[33 + 3.3 (8\sqrt{8})2]

= 2[27 + 72] = 99 × 2 = 198