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

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

x=\sqrt[3]{(\sqrt{2}+1)}-\sqrt[3]{(\sqrt{2}-1)}

; then

x^{3}+3 x=

View answer and explanation

Correct option: A

Option A is correct because the expression simplifies to 2 by cubing x and using the identity

a^3 - b^3 = (a-b)^3 + 3ab(a-b)

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