Question

Solve for u, where u is a real number. (4u+5)^((1)/(3))=(2u-1)^((1)/(3))

Answer 1

To solve for u in the equation \((4u+5)^\frac{1}{3} = (2u-1)^\frac{1}{3}\), we'll raise both sides of the equation to the power of 3 to eliminate the cube roots:

\((4u+5)^\frac{1}{3} = (2u-1)^\frac{1}{3}\)

Now, raise both sides to the power of 3:

\((4u+5)^\frac{1}{3}^3 = (2u-1)^\frac{1}{3}^3\)

This simplifies to:

\(4u+5 = 2u-1\)

Now, isolate the variable u:

Subtract 2u from both sides:

\(4u - 2u + 5 = -1\)

Combine like terms:

\(2u + 5 = -1\)

Subtract 5 from both sides:

\(2u = -1 - 5\)

\(2u = -6\)

Now, divide by 2 to solve for u:

\(u = \frac{-6}{2}\)

\(u = -3\)

So, the solution for u is \(u = -3\).

Explanation: