Question

Which value is a solution of the equation x² = _41?Select all that apply.0A. x = -20B. x = 10C. x = 00D. x = 1Ex=2

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equation

`x^2=(2x)/(x+1)`

STEP 2: Simplify the equation for x

`\begin{gathered} \mathrm{Multiply\:both\:sides\:by\:}x+1 \\ x^2\left(x+1\right)=(2x)/(x+1)\left(x+1\right) \\ \mathrm{Simplify} \\ x^2\left(x+1\right)=2x \end{gathered}`

STEP 3: Solve the resulting polynomial equation

`\begin{gathered} \mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides} \\ x^2\left(x+1\right)-2x=2x-2x \\ x^2\left(x+1\right)-2x=0 \\ Factorise \\ x\left(x-1\right)\left(x+2\right)=0 \\ \mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0 \\ x=0\quad \mathrm{or}\quad \:x-1=0\quad \mathrm{or}\quad \:x+2=0 \\ \mathrm{The\:solutions\:are}: \\ x=0,\:x=1,\:x=-2 \end{gathered}`

Therefore,

`x=0,x=1,x=-2`

Hence, the answers will be as seen below: