Question

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
\[
\boxed{\frac{-7985}{411}} \text{ or approximately } -19.43.
\]