Question

Find the solution of 3 times the square root of the quantity of x plus 5 equals negative 9, and determine if it is an extraneous solution.

Answer 1

The solution is
`x=4`.

Answer 2

Answer: x= 4 is an extraneous solution.

Explanation:

Since we have given that

`3(√(x+5))=-9`

We need to find the extraneous solution.

So, our equation becomes,

`√(x+5)=(-9)/(3)\\\\√(x+5)=-3\\\\\text{On squaring both sides}\\\\x+55=(-3)^2\\\\x+5=9\\\\x=9-5\\\\x=4`

Now, we will check that x = 4 is an extraneous solution.

`3√(4+5)\\eq -9\\\\3√(9)\\eq -9\\\\3* 3\\eq -9\\\\9\\eq -9`

Hence, x= 4 is an extraneous solution.