Question

What is the solution √3x +3 - 1 = x

Answer 1

Answer:

Choice A

Step-by-step explanation:

√(3x +3) - 1 = x

Taking square on both sides:

• $( \sqrt{3x + 2} ) {}^{2} = (x + 1) {}^{2}$
• $3x + 3 = x { }^{2} + 2x + 1$

Subtracting x²+2x + 1 from both sides:

• $3x+3−(x {}^{2} +2x+1)=x {}^{2} +2x+1−(x {}^{2} +2x+1)$
• $3x + 3 - x {}^{2} - 2x - 1 = 0$
• $3x - 2x + 3 - 1 - x {}^{2} = 0$
• $x + 2 - x {}^{2} = 0$

Rewrite as,

• $-x² + x + 2= 0$

Factoring LHS of the equation:[Middle term factor]

• $( - x - 1)(x - 2) = 0$

Now,

• $( - x - 1) = 0 \: \: \: \: \: ...(1)$
• $x - 2 = 0 \: \: \: \: \: ...(2)$

Equation 1:

• $- x - 1 = 0$
• $- x = 0 + 1$
• $- x = 1$
• $x = \boxed{ - 1}$

Equation 2:

• $x - 2 = 0$
• $x = 0 + 2$
• $x = \boxed{2}$

Choice A is accurate.

• -1 & 2