Which of the following is an extraneous solution of square root - 3x-2=x+2?

a) x = - 6

b) x = - 1

c) x = 1

d) x = 6

Hello,

Answer A (x=-6 is an extraneous solution)

√ (-3x-2) = x+2

==>-3x-2>=0

==>x< = - 2/3

So - 3x-2 = (x+2) ²

==>-3x-2=x²+4x+4

==>x²+7x+6=0

==> (x=-6) or (x=-1)

if x=-6 then

√ (-3 * (-6) - 2) = √16=4

-6+2=-4

False 4≠-4

if x=-1

√ (-3 * (-1) - 2) = √1=1

-1+2=1

ok ...