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JEE Advanced2016MathematicsDeterminantsActual

The total number of distinct x ∈ R for which x x 2 1 + x 3 2 x 4 x 2 1 + 8 x 3 3 x 9 x 2 1 + 27 x 3 = 10 is

Correct answer

2

Step-by-step solution

x 3 1 1 1 + x 3 2 4 1 + 8 x 3 3 9 1 + 27 x 3 = 10 ⇒ x 3 1 1 1 1 2 4 1 3 9 + x 3 . x 3 1 1 1 2 4 8 3 9 27 = 10 ⇒ x 3 25 - 23 + 6 x 6 . 2 = 10 ⇒ 6 x 6 + x 3 - 5 = 0 ⇒ x 3 = 5 6 , - 1 Two real solutions for x

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