Question

When solving the radical equation 2 + 20 + 11 = I, the values I =-1 and I = 7 are obtained. Determine if either of these values is a solution of the radical equation. Select the correct two answers. (1 point) Since substituting I = -1 into the original equation resulted in a true statement, I= -1 is a solution to this equation. Since substituting I = 7 into the original equation resulted in a false statement, I = 7 is a not solution to this equation. Since substituting I=-l into the original equation resulted in a false statement, r=-1 is not a solution to this equation. Since substituting I=7 into the original equation resulted in a true statement, I=7 is a solution to this equation.

Answer 1

`\begin{gathered} 2+\sqrt[]{2x+11}=x \\ \text{possible solutions are} \\ x=-1\text{ and x=7} \\ \text{Hence, when x=-1, one has} \\ 2+\sqrt[]{2(-1)+11}=-1 \\ 2+\sqrt[]{-2+11}=-1 \\ 2+\sqrt[]{9}=-1 \\ \text{the root has +3 as solution, then} \\ 2+3=-1\text{ is wrong} \\ \text{then, x=-1 is not a solution} \\ \end{gathered}`
`\begin{gathered} \text{When, x=7 one has} \\ 2+\sqrt[]{2(7)+11}=7 \\ 2+\sqrt[]{14+11}=7 \\ 2+\sqrt[]{25}=7 \\ \text{the square root hassolutions: +5, hence} \\ 2+5=7\Rightarrow7=7\text{ its ok} \\ then,\text{ x=7 is a solution} \\ \end{gathered}`