a-1-3-b-1-3-c-1-3-1-3-1-3-2-1-3-b-c-a-

Question Number 217643 by Rojarani last updated on 17/Mar/25

a^{\frac{1}{3}} + b^{\frac{1}{3}} + c^{\frac{1}{3}} = \frac{1}{3^{\frac{1}{3}} - 2^{\frac{1}{3}}}

b + c - a = ?

Answered by mehdee7396 last updated on 17/Mar/25

\frac{1}{\sqrt[3]{3} - \sqrt[3]{2}} = \sqrt[3]{9} + \sqrt[3]{6} + \sqrt[3]{4} \Rightarrow

a = 9 & b = 6 & c = 4 \Rightarrow b + c - a = 1

o r a = 6 & b = 9 & c = 4 u \Rightarrow b + c - a = 7

o r a = 4 & b = 9 & c = 6 \Rightarrow b + c - a = 11

1 o r 7 o r 11

Commented by Rojarani last updated on 17/Mar/25

S i r t h a n k s .

Answered by Rasheed.Sindhi last updated on 17/Mar/25

a^{\frac{1}{3}} + b^{\frac{1}{3}} + c^{\frac{1}{3}} = \frac{1}{3^{\frac{1}{3}} - 2^{\frac{1}{3}}}

b + c - a = ?

a^{\frac{1}{3}} + b^{\frac{1}{3}} + c^{\frac{1}{3}}

= \frac{1}{3^{\frac{1}{3}} - 2^{\frac{1}{3}}} \cdot \frac{3^{\frac{2}{3}} + 3^{\frac{1}{3}} \cdot 2^{\frac{1}{3}} + 2^{\frac{2}{3}}}{3^{\frac{2}{3}} + 3^{\frac{1}{3}} \cdot 2^{\frac{1}{3}} + 2^{\frac{2}{3}}}

= \frac{9^{\frac{1}{3}} + 6^{\frac{1}{3}} + 4^{\frac{1}{3}}}{{(3^{\frac{1}{3}})}^{3} - {(2^{\frac{1}{3}})}^{3}} = \frac{9^{\frac{1}{3}} + 6^{\frac{1}{3}} + 4^{\frac{1}{3}}}{3 - 2}

= 9^{\frac{1}{3}} + 6^{\frac{1}{3}} + 4^{\frac{1}{3}}

C a s e a = 9

b + c - a = 6 + 4 - 9 = 1 ✓

C a s e a = 6

b + c - a = 9 + 4 - 6 = 7 ✓

C a s e a = 4

b + c - a = 9 + 6 - 4 = 11 ✓

\begin{matrix} \overset{F o r m u l a u s e d}{(A - B) (A^{2} + A B + B^{2}) = A^{3} - B^{3}} \end{matrix}