Question

A student concluded that the solution to the equation √2x+1+3=0 is x=4.

Answer 1

Answer:

I do not agree, because x=4 is an extraneous

Step-by-step explanation:

First, to solve the equation, you subtract 3 from both sides,  then square both sides, subtract one from both sides, and finally divide by 2 on both sides. This indeed gets us x=4, but we also need to check if it's an extraneous solution. To do that we simply plug in x=4 into the original equation. sqrt( 2(4) + 1 ) + 3 = 0. When we do this, we end up with ±3 + 3 = 0. I do not agree, because we don't know if the sqrt(9) is -3 or 3.

Answer 2

Answer:

on Edge

Step-by-step explanation:

I do not agree with the student because there is no real solution.

Solving the equation only gives possible solutions, but you must check them in the original equation.

Checking the solution in the original equation shows that 4 is an extraneous solution.