Solve the equation. Identify any extraneous solutions.

Question

anonymous · Answer

$$8\sqrt{9j}+10=1$$

anonymous · Answer

i think that there is no solution to this am i right?

jdoe0001 · Answer

well, what answer did you get?

anonymous · Answer

$$j= \frac{ 9 }{ 64}$$

anonymous · Answer

$$j= \frac{ 81 }{ 576}$$  thats what i got at first before simplifying

anonymous · Answer

@jdoe0001

jdoe0001 · Answer

mmm one sec

mertsj · Answer

Subtract 10 from both sides to begin with.

mertsj · Answer

$$8\sqrt{9j}+10=1$$

jdoe0001 · Answer

$$8\sqrt(9j)-10+10=1-10$$
$$8\sqrt(9j)=-9$$
$$\sqrt(9j)=\frac{-9}{8}$$
$$9j={(\frac{-9}{8})}^2$$

mertsj · Answer

$$8\sqrt{9j}=-9$$

jdoe0001 · Answer

mmm i get the same, just negative :|, but I'd not say is "extraneous" :)

mertsj · Answer

$$\sqrt{9j}=\frac{-9}{8}$$

anonymous · Answer

i still think there is no solution

mertsj · Answer

Now.  Think.  The radical sign means the principal or positive square root.  So we have a statement that says "the positive square root of 9j is a negative number."

jdoe0001 · Answer

well, is not an imaginary expression for one, unless there's a context into which "J" is not meant to be negative, then, yes

mertsj · Answer

Is that possible?  NO!!  A positive number cannot be negative and there is NO solution.

anonymous · Answer

so i was correct that there is no solution??

mertsj · Answer

If you said there is no solution then you are correct.

anonymous · Answer

yeah i kept saying that lol

mertsj · Answer

Because there is no solution.

mertsj · Answer

Good for you!!