Question

Lincoln and Gemma are looking at the equation sqrt(2x - 3) = sqrt(x). Lincoln says that the solution is extraneous. Gemma says the solution is non-extraneous. Is Lincoln correct? Is Gemma correct? Are they both correct? Justify your response by solving this equation, explaining each step with complete sentences.

Answer 1

@peachpi Please help me, haha. I'm stuck on this and have been for about 45 minutes.

Answer 2

I think there should be a non-extraneous solution. I'd start by dropping the square roots to make the equation linear

Answer 3

2x -3 = x
x=3

Answer 4

This is what I have so far:

sqrt(2x - 3) = sqrt(x)
2x - 3 = x

I used mathway to check what the answer should be and it's 3, so I checked that and it is

sqrt(2(3) - 3) = 3
2(3) - 3 = 3
6 - 3 = 3
3 = 3

Answer 5

What happens to the 2?

Answer 6

It was multiplied by 3 in the simplification

Answer 7

In the part that you did?
2x -3 = x
x=3

Answer 8

I was looking at your work. Where 2(3) - 3 turns into 6 - 3 on the left side

Answer 9

In mine I subtracted x and added 3 to both sides.

Answer 10

Okay, but it yours where does the 2 go?

P.S. I'm sorry, I suck at math

Answer 11

I subtracted the x on the right from 2x.
2x - x = x