Exercise 32 Page 645

We are given three equations. We will find which one of these equations has the same solution set as the radical equation $\sqrt{4}=\sqrt{x+2}.$ To do so, let's first solve the equation $\sqrt{4}=\sqrt{x+2}.$ The solution set of the equation consists of $2.$ We will now solve the equations given in options A, B, and C to find which one has the solution set consisting of $2.$ Let's first consider the equation in A. Notice that we obtained the equation in option C in the third step while solving the equation in option A. Therefore, their solution sets are the same. As we can see, the solution to the equations in A and B is approximately $0.3,$ but not $2.$ It means that it is not the same as the solution of the equation $\sqrt{4}=\sqrt{x+2}.$ Let's now find the solution set of the equation in B. We can see that $2$ is the solution of the equation $4=x+2,$ so this equation has the same solution set as the equation $\sqrt{4}=\sqrt{x+2}.$ Therefore, the correct choice is option B.