Question

What is the solution √3x +3 - 1 = x

Answer 1

Choice A

Explanation:

√(3x +3) - 1 = x

Taking square on both sides:

• 
  `( √(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