Question

Find the solution of 3 times the square root of the quantity of x plus 6 equals negative 12, and determine if it is an extraneous solution.

Answer 1

For this case we have the following equation:

`3 √(x+6)=-12`
Rewriting we have:

`√(x+6)= (-12)/(3)`

`√(x+6)=-4`
We raise both members of the equation to the square:

`(√(x+6))^2=(-4)^2`
Rewriting we have:

`x+6=16`

`x=16-6`

`x=10`
It's a extraneous solution because equality is not met by substituting x = 10 in the original equation:

`3 √(10+6)=-12`

`3 √(16)=-12`

`3(4)=-12`

`12=-12`
Answer:
The solution is:

`x=10`
It's a extraneous solution