Debbie and Trisha are looking at the equation the square root of the quantity of 4 times x minus 6 equals square root of x . Debbie says that the solution is extraneous. Trisha says that the solution is non-extraneous. Is Debbie correct? Is Trisha correct? Are they both correct? Justify your response by solving this equation, explaining each step with complete sentences.

Question

anonymous · Answer

Someone please help! I will reward medal and fan!!

anonymous · Answer

@grex10

anonymous · Answer

Do you get this? @leon549

anonymous · Answer

yeah working on it

anonymous · Answer

extraneous
A solution to an equation that SEEMS to be right, but when we check it (by substituting it into the original equation) turns out NOT to be right.

anonymous · Answer

So then who is correct?

anonymous · Answer

@lilcj2001

anonymous · Answer

attachment

anonymous · Answer

i will go with debbie

anonymous · Answer

Why?

anonymous · Answer

the equation will become 4x -6= sqrt x

anonymous · Answer

square both sides to get a general equation

xapproachesinfinity · Answer

hey there, let's work it out and find what is happening

xapproachesinfinity · Answer

$$\sqrt{4x-6}=\sqrt{x}$$ this is our equation yes

xapproachesinfinity · Answer

as leon said we take square of both sides to solve this

xapproachesinfinity · Answer

$$(\sqrt{4x-6})^2=(\sqrt{x})^2 \Longrightarrow 4x-6=x $$
$$4x-x=-6$$
can you solve this one?

xapproachesinfinity · Answer

should be 4x-x=6 not -6 sorry

xapproachesinfinity · Answer

$$4x-x=6 $$

xapproachesinfinity · Answer

so can you solve it or need help with that one?

xapproachesinfinity · Answer

well @LexiLuvv2431  what do say?

anonymous · Answer

Heyy thank you. Umm I kinda think I get it but at the same time I dont know where to start.