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The total number of distinct x R ∈ for which |(x, x^2, 1 + x^2), (2x, 4x^2, 1 + 8x^3), (3x, 9x^2, 1 + 27x^3)| = 10 is _________.

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The total number of distinct x R ∈ for which |(x, x2, 1 + x2), (2x, 4x2, 1 + 8x3), (3x, 9x2, 1 + 27x3)| = 10 is  _________.

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It is given that

Therefore, x = −1 and (5/6)1/3.

Hence, there are two district values for x. Thus, 2 is the answer.

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