Question

i need a little help. please use evidence and steps leading to answer. I asks to find the error in one or more of the steps and explain why its wrong

Answer 1

To identify the error in the procedure shown in the picture, it is important to remember the following:

`\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ (a-b)^2=a^2-2ab+b^2 \end{gathered}`

Keeping this on mind, you can solve the given equation as following:

1. Given:

`\sqrt[]{5x}=x+2`

2. Square both sides of the equation:

`\begin{gathered} (\sqrt[]{5x})^2=(x+2)^2 \\ 5x=x^2+2(x)(2)+2^2 \\ 5x=x^2+4x+4 \end{gathered}`

3. Move the the term on the left side to the right side and add like terms:

`0=x^2-x+4`

4. Apply the Quadratic formula to find "x":

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ x=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(1)(4)}}{2(1)} \\ \\ x_1=(1)/(2)(i-\sqrt[]{15)} \\ \\ x_2=(1)/(2)(i+\sqrt[]{15)}_{} \end{gathered}`

Therefore, you can identify that the error is in Step C, because:

`(x+2)^2=x^2+4x+4`