FREE MEDAL WITH BEST ANSWER

John and Tim are looking at the equation the square root of the quantity of 3 times x plus 4 equals square root of x . John says that the solution is extraneous. Tim says the solution is non-extraneous. Is John correct? Is Tim correct? Are they both correct? Justify your response by solving this equation, explaining each step with complete sentences.

Question

FREE MEDAL WITH BEST ANSWER

John and Tim are looking at the equation the square root of the quantity of 3 times x plus 4 equals square root of x . John says that the solution is extraneous. Tim says the solution is non-extraneous. Is John correct? Is Tim correct? Are they both correct? Justify your response by solving this equation, explaining each step with complete sentences.

anonymous · Answer

@SBurchette please take a look?

anonymous · Answer

@TammisaurusRex take a look?

sburchette · Answer

So, we have that $$\sqrt{3x+4}=\sqrt{x}$$ If we square both sides, we have $$3x+4=x$$Solving for x, we get x=-2. Substituting into the original equation, we get $$\sqrt{-2}=\sqrt{-2}$$ Since the solution gives us a nonreal number, we conclude that the solution is extraneous.

anonymous · Answer

Thank you so much! I'm glad you explained. Now I'm awarding you a medal hehe. :)

anonymous · Answer

Thanks this helped alot