Question

Given the equation Square root of 2x plus 1 = 3, solve for x and identify if it is an extraneous solution. ^ I really don't understand this topic, whatsoever. Could someone help?

Answer 1

`x=4`

Explanation:

We have been given a square root equation
`√(2x+1)=3`. We are asked to solve for x.

To solve our given equation, we will square both sides of our given equation as:

`(√(2x+1))^2=3^2`

Using radical rule
`\sqrt[n]{a^n} =a`, we will get:

`2x+1=9`

Upon subtracting 1 from both sides, we will get:

`2x+1-1=9-1`

`2x=8`

Now, we will divide both sides of our equation by 2.

`(2x)/(2)=(8)/(2)`

`x=4`

We know that to find an extraneous solution, we need to substitute back the solution in original equation to check that if it satisfies original equation or not. If the solution does not satisfy original equation, then it is an extraneous solution.

`√(2*4+1)=3`

`√(8+1)=3`

`√(9)=3`

`3=3`

Since both sides of our given equation are equal, therefore,
`x=4` is not an extraneous solution.

Answer 2

The equation given above is  sqrt (2x + 1) = 3. First, square both sides of the equation giving, 2x + 1 = 9. Solving for x in this equation gives an answer of x = 4. When we substitute x = 4 to the original equation, the number inside the radical sign is positive. Thus, x = 4 and it is a non-extraneous root.