To solve the equation \((x-3)^{2/5} = 20\), let's go through the questions step by step.
1. What should be the first step when solving the quadratic equation above?
The first step is to eliminate the exponent by raising both sides to the power of \(\frac{5}{2}\). This will remove the \(\frac{2}{5}\) exponent on the left side.
2. Which of the following is one of the solutions to the quadratic equation above?
After applying the first step, we would have:
\[
x - 3 = 20^{5/2}
\]
Therefore:
\[
x = 20^{5/2} + 3
\]
Calculating \(20^{5/2}\) would give one of the solutions.
3. Which of the following is the other solution to the quadratic equation above?
The equation could produce two solutions, one from the positive and one from the negative root of the \((x-3)\) term. Therefore the other solution can be obtained from:
\[
x - 3 = -20^{5/2}
\]
This leads to:
\[
x = -20^{5/2} + 3
\]
As you didn't provide specific options, I can't specify exact numerical values for the solutions. But the methods to derive the solutions are noted. You would calculate \(20^{5/2}\) to find the numerical answers for both solutions.
Would you like to see the calculation for \(20^{5/2}\)?
1 answer