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

Question

The total number of distinct x ∈ R for which |x x2 1+x3 2 x 4 x2 1+8 x3 3 x 9 x2 1+27 x3|=10 is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

|x x2 1+x3 2 x 4 x2 1+8 x3 3 x 9 x2 1+27 x3|=10 ⇒ |x x2 1 2 x 4 x2 1 3 x 9 x2 1|+|x x2 x3 2 x 4 x2 8 x3 3 x 9 x2 27 x3|=10 ⇒ x 3|1 1 1 2 4 1 3 9 1|+ x 6|1 1 1 2 4 8 3 9 27|=10 ⇒ 2 x 3+12 x 6=10 ⇒ 6 x 6+ x 3-5=0 ⇒ (6 x 3-5)( x 3+1)=0 ⇒ x 3=(5/6), x 3=-1 So two real roots

Q. The total number of distinct x∈R for which ∣∣​x2x3x​x24x29x2​1+x31+8x31+27x3​∣∣​=10 is

Q. The total number of distinct $x \in R$ for which $∣ ∣ x 2 x 3 x x^{2} 4 x^{2} 9 x^{2} 1 + x^{3} 1 + 8 x^{3} 1 + 27 x^{3} ∣ ∣ = 10$ is