Question

Which of the following is true about the solution(s) to the equation:

Answer 1

We have the equation:

`x=\sqrt[]{2x+3}`

We take the square on both sides:

`\begin{gathered} x^2=2x+3 \\ x^2-2x-3=0 \end{gathered}`

Factoring the quadratic equation leads to:

`(x-3)(x+1)=0`

It seems like the solutions are x = 3 and x = -1, but we need to evaluate them first. Using them in the original equation:

`\begin{gathered} x=3\colon3=\sqrt[]{2\cdot3+3}\Rightarrow3=\sqrt[]{9}\Rightarrow3=3\text{ (Correct)} \\ x=-1\colon-1=\sqrt[]{2\cdot(-1)+3}\Rightarrow-1=\sqrt[]{1}\Rightarrow-1=1\text{ (Incorrect)} \end{gathered}`

We conclude that x = 3 is the only solution to the equation.