√(x-1) +√(x+2) = √(2x-3) x=?

Question

`√(x-1) +√(x+2) = √(2x-3)` x=?

Answer 1

`x = ( - 2 + - √( - 176) )/(10)`

Explanation:

attached

Answer 2

• x = 2

Explanation:

See the steps:

• 
  `√(x-1) +√(x+2) =√(2x-3)`
• x - 1 + x + 2 + 2
  `\sqrt{({x-1)(x+2)}` = 2x - 3
• 2x + 1 + 2
  `√(x^2+x -2)` = 2x - 3
• 2
  `√(x^2+x -2)}` = -4
• 
  `√(x^2+x-2)` = -2
• x² + x - 2 = 4
• x² + x - 6 = 0
• x = (-1 ±
  `√(1-4(-6))`)/2
• x = (-1 ± 5)/2
• x = -3, discounted as it leads to negative root
• x = 2