Question

Which of the following is an extraneous solution of (45-3x)^1/2=x-9?

Answer 1

Answer:

The answer is C: X = 3

Step-by-step explanation:

Answer 2

Answer:

An extraneous solution of the given expression is 3 and 12.

Step-by-step explanation:

Given : Expression $(45-3x)^{\frac{1}{2}}=x-9$

To find : An extraneous solution of given expression ?

Solution :

First we solve the given expression algebraically,

$(45-3x)^{\frac{1}{2}}=x-9$

Squaring both side,

$(45-3x)^{\frac{2}{2}}=(x-9)^2$

$45-3x=x^2-18x+81$

$x^2-18x+81-45+3x=0$

$x^2-15x+36=0$

Solving quadratic equation,

$x^2-3x-12x+36=0$

$x(x-3)-12(x-3)=0$

$(x-3)(x-12)=0$

$x=3 \text{ or } x=12$

Therefore, An extraneous solution of the given expression is 3 and 12.