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Question: If \(x = \sqrt[3]{(\sqrt{2} + 1)} - \sqrt[3]{(\sqrt{2} - 1)};\) then \(x^{3} + 3x =\)...

If x=(2+1)3−(2−1)3;x = \sqrt[3]{(\sqrt{2} + 1)} - \sqrt[3]{(\sqrt{2} - 1)}; then x3+3x=x^{3} + 3x =

A

2

B

6

C

6x

D

None of these

Answer

2

Explanation

Solution

x=(2+1)1/3−(2−1)1/3x = (\sqrt{2} + 1)^{1/3} - (\sqrt{2} - 1)^{1/3}

x3=2−3(2−1)1/3x⇒x3+3x=2x^{3} = 2 - 3(2 - 1)^{1/3}x \Rightarrow x^{3} + 3x = 2.