manhhieu07
Answered

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[tex]\sqrt{x-1} +\sqrt{x+2} = \sqrt{2x-3}[/tex] x=?

Sagot :

Tasyha

Answer:

[tex]x = \frac{ - 2 + - \sqrt{ - 176} }{10} [/tex]

Step-by-step explanation:

attached

View image Tasyha
mhanifa

Answer:

  • x = 2

Step-by-step explanation:

See the steps:

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