Question

HELP
Solve. Check for extraneous solutions sqrt 3x = sqrt x+6

Answer 1

X=3

Explanation:

Solve. Check for extraneous solutions.

√3x = √x+6

Raise both sides to the second power

(√3x)2 = (√x+6)2

After squaring

3x = x+6

Rearranged equation

2x -6 = 0

Add 6 to both sides

2x = 6

Divide both sides by 2:

x = 3

Answer 2

`Domain:\\\\\left\begin{array}{ccc}3x\geq0\to x\geq0\\x+6\geq0\to x\geq-6\end{array}\right\}\text{therefore}\ x\geq0\to x\in[0,\ \infty)\\\\------------------------\\\\√(3x)=√(x+6)\qquad\text{square of both sides}\\\\(√(3x))^2=(√(x+6))^2\qquad\text{use}\ (√(a))^2=a\ \text{for}\ a\geq0\\\\3x=x+6\qquad\text{subtract x from both sides}\\\\2x=6\qquad\text{divide both sides by 2}\\\\\boxed{x=3}\in D`