Question

The number of solutions of the equation $\dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}$ is

• A. $0$
• B. $6$
• C. $9$
• D. $∞$
• E. $3$

Answer 1

Answer: (C)

$9$

Answer 2

$\dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}$

⇒$$[\dfrac{1}{2}(x^3+1)]^{3}=2x-1

$⇒[\dfrac{1}{8}(x^9+3x^6+3x^3+1)]=2x-1$

$⇒[\dfrac{1}{8}(x^9+3x^6+3x^3+1)]=2x-1$

$⇒[\dfrac{1}{8}(x^9+3x^6+3x^3-2x+9)=0$

Hence this polynomial of degree $9$ has $9$ solutions.(_Ans.)