Question

Any help is appreciated! Solve the equation for x. Identify any extraneous solutions. √x=-3 I know the answer is (+9) but is (-9) an extraneous solution? I'm not sure what an extraneous solution is. Thanks!

Answer 1

an extraneous solution is basically a value that seems to work when solving an equation, when in reality it doesn't work

Answer 2

for this problem, you can't have a negative value under a square root sign, so -9 should not be a solution

Answer 3

So it is NOT an extraneous solution? @11calcBC

Answer 4

if my memory is accurate, yes

Answer 5

Thanks!

Answer 6

somebody confirm this...

Answer 7

Can you confirm this @tkhunny ?

Answer 8

\(\sqrt{x} = -3\)

You do NOT know the answer is x = +9. That is incorrect. The answer is also not x = -9.

This equation has no solution in the Real Numbers.

The Domain if \(f(x) = \sqrt{x}\) is \(x \ge 0\). This eliminates \(x = -9\)
The Range if \(f(x) = \sqrt{x}\) is \(f(x) \ge 0\). This eliminates \(x = 9\)

Answer 9

\(\sqrt{9} = 3 \ne -3\)

Answer 10

Thanks again @11calcBC !!!

Answer 11

no problem :D

Answer 12

What was your final answer?