What is the answer to a^{1/3}=26^{1/3}+7^{1/3}+63^{1/3} ?

The answer to a^{1/3}=26^{1/3}+7^{1/3}+63^{1/3} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

a^{1/3}=26^{1/3}+7^{1/3}+63^{1/3}

a^{\frac{1}{3}} = 2 6^{\frac{1}{3}} + 7^{\frac{1}{3}} + 6 3^{\frac{1}{3}}

a = 96 + 3 \cdot 7^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 6 3^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 7^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}} + 6 \cdot 23 4^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 6 \cdot 7 8^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 21 \cdot 9^{\frac{1}{3}} + 42 \cdot 3^{\frac{1}{3}} + 7 \cdot 9^{\frac{2}{3}} + 6 3^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}}

Decimal Notation

a = 694.20836 \dots

Solution steps

a^{\frac{1}{3}} = 2 6^{\frac{1}{3}} + 7^{\frac{1}{3}} + 6 3^{\frac{1}{3}}

Take both sides of the equation to the power of

3 : a = 96 + 3 \cdot 7^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 6 3^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 7^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}} + 6 \cdot 23 4^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 6 \cdot 7 8^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 21 \cdot 9^{\frac{1}{3}} + 42 \cdot 3^{\frac{1}{3}} + 7 \cdot 9^{\frac{2}{3}} + 6 3^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}}

a = 96 + 3 \cdot 7^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 6 3^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 7^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}} + 6 \cdot 23 4^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 6 \cdot 7 8^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 21 \cdot 9^{\frac{1}{3}} + 42 \cdot 3^{\frac{1}{3}} + 7 \cdot 9^{\frac{2}{3}} + 6 3^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}}

Verify Solutions:

a = 96 + 3 \cdot 7^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 6 3^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 7^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}} + 6 \cdot 23 4^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 6 \cdot 7 8^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 21 \cdot 9^{\frac{1}{3}} + 42 \cdot 3^{\frac{1}{3}} + 7 \cdot 9^{\frac{2}{3}} + 6 3^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}}

True

The solution is

a = 96 + 3 \cdot 7^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 6 3^{\frac{1}{3}} \cdot 2 6^{\frac{2}{3}} + 3 \cdot 7^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}} + 6 \cdot 23 4^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 6 \cdot 7 8^{\frac{1}{3}} \cdot 7^{\frac{2}{3}} + 21 \cdot 9^{\frac{1}{3}} + 42 \cdot 3^{\frac{1}{3}} + 7 \cdot 9^{\frac{2}{3}} + 6 3^{\frac{2}{3}} \cdot 2 6^{\frac{1}{3}}

x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} - 36 = 0

5 + x + 14 = x + 34

3 x - 10 = 2

2 x^{2} + 5 x - 5 = 0

4 \frac{x}{( x + 1 )} + 3 \frac{( x + 1 )}{x} = 8

What is the answer to a^{1/3}=26^{1/3}+7^{1/3}+63^{1/3} ?
The answer to a^{1/3}=26^{1/3}+7^{1/3}+63^{1/3} is
Solve for a: a^{1/3}=26^{1/3}+7^{1/3}+63^{1/3}
The solution is