Question

Find the solution of 3 sqrt x+5 = -9 and determine if it is an extraneous solution

x = 4 ; not extraneous
x = 4 ; extraneous
x = 0 ; extraneous
x = 0 ; not extraneous

Answer 1

\[3\sqrt{x + 5}=-9\] is what the question looks like

Answer 2

@freckles please help I don't understand what this is

Answer 3

well we can solve this equation..take 3 to rhs, square both sides blah blah...

but look at the equation carefully, we cannot get a negative value for square root. although we can solve for x and find a number, it is 'extraneous'

Answer 4

? i don't understand what that means. the solution is extraneous? but what does x equal?

Answer 5

ok...lets first solve for x
\(\\\sqrt{x+5} = -3 \\square~ both ~sides\\ x+5=9\\x=4\)

Answer 6

followed?

Answer 7

yeah okay ! so it's the second one, x = 4 extraneous

Answer 8

do you understand why its extraneous?

Answer 9

something to do with the solution right like its not proven right

Answer 10

yep,
so we have \( \sqrt{x+5}=-3\)

do you know any number whose square root is negative?

Answer 11

no...

Answer 12

because there isnt...
this equation actually has no solution.
but we have somehow solved for x using correct mathematical operations.
that is why the solution is called 'extraneous'