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 =…

The total number of distinct x∈R for which xx21+x32x4x21+8x33x9x21+27x3=10 is

Solution

x3111+x3241+8x3391+27x3=10
⇒ x3111124139+x3. x3 1112483927=10
⇒ x325-23+6x6.2=10
⇒ 6x6+x3-5=0
⇒ x3=56, -1
Two real solutions for x

Asked in: JEE Advanced 2016 (Paper 1)

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