The question asks to transform the formula $a^3 + b^3 + c^3 = d^3$ to solve for $b$.

Here’s the solution:

1. Start with the equation: $a^3 + b^3 + c^3 = d^3$

2. Isolate $b^3$ by subtracting $a^3$ and $c^3$ from both sides: $b^3 = d^3 - a^3 - c^3$

3. Solve for $b$ by taking the cube root of both sides: $b = \sqrt[3]{d^3 - a^3 - c^3}$

The transformed formula is: $b = \sqrt[3]{d^3 - a^3 - c^3}$

Would you like further explanations or examples of how to use this formula?

Related Questions

1. How would the solution change if solving for $c$ instead of $b$?
2. What are the conditions for real solutions of $b$ in this equation?
3. Can you apply this formula to a specific numerical example (e.g., $a = 1, c = 2, d = 3$)?
4. What does this equation represent geometrically or in terms of algebraic theory?
5. What happens to $b$ if $d^3 < a^3 + c^3$?

Tip

When solving equations with cube roots, consider the possibility of complex roots if the expression inside the root becomes negative.