Solve the cube root equation 411x−15−−−−−−−√3+21=1

Answer 1

To solve the equation \( \sqrt[3]{411x - 15} + 21 = 1 \), we start by isolating the cube root term.

1. Subtract 21 from both sides: \[ \sqrt[3]{411x - 15} = 1 - 21 \] \[ \sqrt[3]{411x - 15} = -20 \]

2. Cube both sides to eliminate the cube root: \[ 411x - 15 = (-20)^3 \] \[ 411x - 15 = -8000 \]

3. Add 15 to both sides: \[ 411x = -8000 + 15 \] \[ 411x = -7985 \]

4. Divide both sides by 411: \[ x = \frac{-7985}{411} \]

5. Calculate the division: \[ x \approx -19.43 \]

Thus, the solution to the equation \( \sqrt[3]{411x - 15} + 21 = 1 \) is \[ \boxed{\frac{-7985}{411}} \text{ or approximately } -19.43. \]