Question

Given the equation Square root of 2x plus 1 = 3, solve for x and identify if it is an extraneous solution.

x = 4, solution is extraneous

x = 4, solution is not extraneous

x = 5, solution is extraneous

x = 5, solution is not extraneous

Answer 1

It's 4 but how do you know if it's extraneous or not?

Answer 2

Plug it back into the original equation. If you get \(\sqrt{\text{negative number}}\), it's an extraneous solution.

Answer 3

2(4) + 1 = 3?

2(4) + 1 = 9?

So it would be?

Answer 4

Think I'm doin something wrong :p

Answer 5

No, it's not extraneous:
\[\sqrt{2x+1}~~\Rightarrow~~\sqrt{8+1}=\sqrt{9}=\sqrt{\text{positive number}}\]

Answer 6

Ok I get it, thanks

Answer 7

yw