Question

A student concluded that the solution to the equation √2x+1+3=0 is x=4.
Do you agree? Explain why or why not?

Answer 1

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.

Answer 2

We want to see if a given solution for a given equation is correct or not.

We will see that the solution is incorrect, as the equation does not have real solutions.

Let's see how to conclude that:

Here we start with the equation:

$\sqrt{2x + 1} + 3 = 0$

And the student for some reason says that the solution is x = 4, so let's see that.

If we replace by x = 4 we get:

$\sqrt{2*4 + 1} + 3 = 0\\\sqrt{9} + 3 = 0\\3 + 3 = 0\\6 = 0$

Which is false, thus the solution is wrong.

Why does this happen?

Because there are no real solutions for our equation.

The square root is always positive, so if we have a sum between a square root and a positive number, is impossible to get 0.

Also, below you can see the graph of our equation, and you will see that it never crosses the x-axis, thus, it is never equal to zero.

If you want to learn more, you can read:

https://brainly.com/question/4526506