If \(\rm a^{\frac{1}{3}}+b^{\frac{1}{3}}+c^{\frac{1}{3}}=0\), then the value of (a + b + c)³ = ?

Question

Question

This question was previously asked in

OSSC CGLRE (Mains) Exam (Mathematics) Official Paper (Held On: 23 July, 2023)

Answer 1

Given:

\(\rm a^{\frac{1}{3}}+b^{\frac{1}{3}}+c^{\frac{1}{3}}=0\)

Formula used:

If \(\rm a^{\frac{1}{3}}+b^{\frac{1}{3}}+c^{\frac{1}{3}}=0\), then

\(\rm a + b + c = 3\left(a^{\frac{1}{3}} \times b^{\frac{1}{3}} \times c^{\frac{1}{3}}\right)\)

Calculation:

\(\rm (a + b + c)^3 = \left[3\left(a^{\frac{1}{3}} \times b^{\frac{1}{3}} \times c^{\frac{1}{3}}\right)\right]^3\)

⇒ (a + b + c)³ = 27abc

∴ The value of (a + b + c)³ = 27abc