Question

Square root of x + 22 = x + 2

Answer 1

(a) 3

(b) -6

Explanation:

We have the following equation:

`√(x+22)=x+2`

We solve for x:

`\begin{gathered} \left(√(x+22)\right)^2=\left(x+2\right)^2 \\ \\ x+22=x^2+4x+4 \\ \\ x^2+4x-x+4-22=0 \\ \\ x^2+3x-18=0 \\ \\ \left(x-3\right)\left(x+6\right)=0 \\ \\ x-3=0\rightarrow x=3 \\ \\ x+6=0\rightarrow x=-6 \\ \\ \text{ We check the solutions} \\ \\ √(3+22)=3+2\rightarrow√(25)=5\rightarrow5=5\rightarrow\text{ True} \\ \\ √(\left(-6\right)+22)=\left(-6\right)+2\rightarrow√(16)=-4\rightarrow4=-4\rightarrow\text{ False} \end{gathered}`

Therefore:

(a) The only correct answer is x = 3

(b) The extraneous response is x = -6