Respuesta :

mhanifa

Answer:

  • A) a = 4, b = 3

Step-by-step explanation:

#6

Given equation:

  • 4/(x - 3) + 2/(x - 2) = 2

Multiply all terms by (x - 3)(x - 2):

  • 4(x - 2) + 2(x - 3) = 2(x - 3)(x - 2)
  • 2(x - 2) + (x - 3) = (x - 3)(x - 2)
  • 2x - 4 + x - 3 = x² - 5x + 6
  • x² - 5x - 3x + 6 + 7 = 0
  • x² - 8x + 13 = 0
  • x = (8 ± √(8² - 4*13))/2 = (8 ± √12)/2 = (8 ± 2√3)/2 = 4 ± √3

Compare this to the given form to get:

  • a = 4, b = 3

Correct choice is A
  • 4/x-3+2/x-2=2
  • [4(x-2)+2(x-3)]/(x-3)(x-2)=2
  • 4x-8+2x-6=2(x²-2x-3x+6)
  • 4x-8+2x-6=2x²-10x+12
  • 6x-14=2x²-10x+12
  • 3x-7=x²-5x+6
  • x²-8x+13=0

On solving

x=4±√3

So

a=4 and b=3

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