Question

What values if x are solutions of the equation. square root 1 - X squared plus 2 equals 3

Answer 1

We have to find the values of x that are solution for the equation

`√(1-x^2)+2=3`

To solve this equation, the first thing we will do is pass, the 2 that is on the left side, to the right side with the opposite sign

`\begin{gathered} √(1-x^2)=3-2 \\ \\ √(1-x^2)=1 \end{gathered}`

Now we will take power two, on both sides of the equation

`\begin{gathered} (√(1-x^2))^2=1^2 \\ \\ 1-x^2=1 \end{gathered}`

Now we will pass the x square to the rigth with opposite sign, and the 1 on the right to the left with opposite sign

`\begin{gathered} 1-1=x^2 \\ \\ 0=x^2 \end{gathered}`

Finally, we take square root on both sides to find

`\begin{gathered} \pm√(0)=√(x^2) \\ \\ \pm0=x \end{gathered}`

Where we have to include both square roots, the positive and the negative one. In this specific case, both are the same, because the solution is 0. Therefore, we conclude:

`x=0`

We conclude that the provided equation has a unique solution, and that this solution is 0.