Answer:
Choice A
Step-by-step explanation:
√(3x +3) - 1 = x
Taking square on both sides:
- [tex]( \sqrt{3x + 2} ) {}^{2} = (x + 1) {}^{2} [/tex]
- [tex]3x + 3 = x { }^{2} + 2x + 1[/tex]
Subtracting x²+2x + 1 from both sides:
- [tex]3x+3−(x {}^{2} +2x+1)=x {}^{2} +2x+1−(x {}^{2} +2x+1)[/tex]
- [tex]3x + 3 - x {}^{2} - 2x - 1 = 0[/tex]
- [tex]3x - 2x + 3 - 1 - x {}^{2} = 0[/tex]
- [tex]x + 2 - x {}^{2} = 0[/tex]
Rewrite as,
- [tex]-x² + x + 2= 0[/tex]
Factoring LHS of the equation:[Middle term factor]
- [tex]( - x - 1)(x - 2) = 0[/tex]
Now,
- [tex]( - x - 1) = 0 \: \: \: \: \: ...(1)[/tex]
- [tex]x - 2 = 0 \: \: \: \: \: ...(2)[/tex]
Equation 1:
- [tex] - x - 1 = 0[/tex]
- [tex] - x = 0 + 1[/tex]
- [tex] - x = 1[/tex]
- [tex]x = \boxed{ - 1}[/tex]
Equation 2:
- [tex]x - 2 = 0[/tex]
- [tex]x = 0 + 2[/tex]
- [tex]x = \boxed{2}[/tex]
Choice A is accurate.
