Answer:
[tex]\displaystyle x=\sqrt{\frac{2U}{k}}[/tex]
The third option is the correct answer.
Step-by-step explanation:
Equation Solving
We have the following equation:
[tex]\displaystyle U=\frac{1}{2}kx^2[/tex]
And it's required to solve it for x.
To solve this equation we need to perform some operations to have the x isolated from any other variables, constants, or operations.
This will be done by conveniently operating on both sides as follows:
Eliminate the denominator by multiplying by 2:
[tex]\displaystyle 2U=kx^2[/tex]
Move k to the other side by dividing by k:
[tex]\displaystyle \frac{2U}{k}=x^2[/tex]
Swapping sides to have x at the left side:
[tex]\displaystyle x^2=\frac{2U}{k}[/tex]
Taking the square root:
[tex]\mathbf{\displaystyle x=\sqrt{\frac{2U}{k}}}[/tex]
The third option is the correct answer.
