Question

### Gauthmathier7887

Grade 10 · 2020-11-04

What is the sum of the solutions of (2x-1)^{2}=(x+2)^{2}?

Good Question (578)

Answer

4.7(173) votes

### Gauthmathier6496

Grade 10 · 2020-11-04

Answer

\dfrac{8}{3}.

Explanation

If a and b are real numbers and a^{2}=b^{2}, then either a=b or a=-b. Since (2x-1)^{2}=(x+2)^{2}, either 2x-1=x+2 or 2x-1=-(x+2). In the first case, x=3, and in the second case, 3x=-1, or x=-\dfrac{1}{3}. Therefore, the sum of the solutions x of (2x-1)^{2}=(x+2)^{2} is 3+\left(-\dfrac{1}{3}\right)=\dfrac{8}{3}.

Thanks (122)

Does the answer help you? Rate for it!

## Still Have Questions?

Find more answers or ask new questions now.