Question

Total number of real values of x such that $\frac{(12+x{)}^{\frac{1}{7}}}{x}+\frac{(12+x{)}^{\frac{1}{7}}}{12}=\frac{64}{3}{x}^{\frac{1}{7}}$ is/are

• A. zero
• B. one
• C. seven
• D. two

Answer 1

The correct option is B

one

$\frac{(12+x{)}^{\frac{1}{7}}}{x}+\frac{(12+x{)}^{\frac{1}{7}}}{12}=\frac{64}{3}{x}^{\frac{1}{7}}\Rightarrow (12+x)(12+x{)}^{\frac{1}{7}}=4.(64).x.x^{\frac{1}{7}}=2^8.x^{\frac{8}{7}}\Rightarrow 12+x=x(2^8{)}^{\frac{7}{8}}\therefore x=\frac{12}{127}$