Question

$\frac{4}{9^{\frac{1}{3}}-3^{\frac{1}{3}}+1}$ is equal to

• A. $3^{\frac{1}{3}}+1$
• B. $3^{\frac{1}{3}}-1$
• C. $3^{\frac{1}{3}}+2$
• D. $3^{\frac{1}{3}}-2$

Answer 1

The correct option is A $3^{\frac{1}{3}}+1$

$4=3+1$

$4=3^{\frac{3}{3}}+1^3$

$4=(3^{\frac{1}{3}}+1)(3^{\frac{2}{3}}-3^{\frac{1}{3}}+1)$

$4=(3^{\frac{1}{3}}+1)(9^{\frac{1}{3}}-3^{\frac{1}{3}}+1)$

$\therefore \frac{(3^{\frac{1}{3}}+1)(9^{\frac{1}{3}}-3^{\frac{1}{3}}+1)}{9^{\frac{1}{3}}-3^{\frac{1}{3}}+1}$

$⟹3^{\frac{1}{3}}+1$