Question

Find the solution of 3 square root x+6 =-12, and determine if is an extraneous solution

Answer 1

Answer: The solution to the above expression is 10.

It is not extraneous solution, as it not satisfying the equation.

Explanation:

Since we have given that

3 square root x+6 =-12

that means,

`3√(x+6)=-12`

We just need to find the value of x:

`3√(x+6)=-12\\\\√(x+6)=(-12)/(3)\\\\√(x+6)=-4\\\\\text{ On squaring both sides, we get}\\\\x+6=(-4)^2\\\\x+6=16\\\\x=16-6\\\\x=10`

Hence, the solution to the above expression is 10.

Now, we have to check whether it is extraneous solution or not.

Put x= 10 in the above expression,

`3√(10+6)=-12\\\\3√(4)=-12\\\\3* 4=-12\\\\12\\eq -12`

Hence, it is not extraneous solution, as it not satisfying the equation.