Question
Answer the questions about this quadratic equation shown below.
(x−3)2^/5 =20
(3 points)
What should be the first step when solving the quadratic equation above?___
Which of the following is one of the solutions to the quadratic equation above? ___
Which of the following is the other solution to the quadratic equation above? ___
(x−3)2^/5 =20
(3 points)
What should be the first step when solving the quadratic equation above?___
Which of the following is one of the solutions to the quadratic equation above? ___
Which of the following is the other solution to the quadratic equation above? ___
Answers
GPT-4o mini
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. 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 \(20^{5/2}\)?