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Official 2022 Paper 1 · Q13

Paper 1Algebra

Given that

(a3+2b3)(2a3−b3)=2\left(a^3+\frac2{b^3}\right)\left(\frac2{a^3}-b^3\right)=\sqrt2

where aa and bb are real numbers, what is the least value of abab?

A−2-\sqrt2
B2\sqrt2
C−22-2\sqrt2
D222\sqrt2
E−22-\frac{\sqrt2}2
F22\frac{\sqrt2}2
G−21/6-2^{1/6}
H21/62^{1/6}

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