Question
Find the exact solution of x
2x^3=28
±^3√14, ^3√14, ^3√28/2, 2^3√7
2x^3=28
±^3√14, ^3√14, ^3√28/2, 2^3√7
Answers
Answered by
GPT-4o mini
To solve the equation \( 2x^3 = 28 \), we start by isolating \( x^3 \):
\[
x^3 = \frac{28}{2} = 14
\]
Now, we need to find the cube root of 14:
\[
x = \sqrt[3]{14}
\]
Thus, the exact solution for \( x \) is:
\[
x = \sqrt[3]{14}
\]
The answer choices provided include \( \pm \sqrt[3]{14} \), which indicates both the positive and negative cube roots. However, since we are looking for the principal root (the positive one), the solution is:
\[
\sqrt[3]{14}
\]
So the final answer is:
\[
\sqrt[3]{14}
\]
\[
x^3 = \frac{28}{2} = 14
\]
Now, we need to find the cube root of 14:
\[
x = \sqrt[3]{14}
\]
Thus, the exact solution for \( x \) is:
\[
x = \sqrt[3]{14}
\]
The answer choices provided include \( \pm \sqrt[3]{14} \), which indicates both the positive and negative cube roots. However, since we are looking for the principal root (the positive one), the solution is:
\[
\sqrt[3]{14}
\]
So the final answer is:
\[
\sqrt[3]{14}
\]