Question

Roziąż równiania kwadratowe:

a) (2x-1)(2x+1)-(4x+5)*=-4x-2

b)(x+3)*-2(x-2)*=4x+10

Odpowiedzi: w przykładzie a) -1,-2 b) 1,9

Answer 1

a)

(2x-1)(2x+1)-(4x+5)²=-4x-2

 4x² - 1 – (16x²+ 40x + 25) = -4x -2

4x²- 1 -16x² -40x -25 +4x + 2=0

-12x² -36x -24 =0  /: (-12)

x² + 3x + 2 = 0

 

Δ= b² - 4ac = 3² - 4*1*2 = 9-8 =1

√Δ = √1 = 1

x₁ = (-b-√Δ)/2a = (-3-1)/2 = -4/2 = -2

x₂ = (-b+√Δ)/2a = (-3+1)/2 = -2/2 =-1

 

b)

(x+3)²-2(x-2)²=4x+10

x² + 6x + 9 – 2(x² -4x+4) = 4x +10

 x² + 6x + 9 – 2x²+ 8x- 8 - 4x - 10 = 0

-x² +10x  -9 = 0  /*(-1)

x² -10x +9 = 0

Δ= b² - 4ac = (-10)² - 4*1*9 = 100 – 36 = 64

√Δ = √64 = 8

x₁ = (-b-√Δ)/2a = (10-8)/2 = 2/2 = 1

x₂ = (-b+√Δ)/2a = (10+8)/2 = 18/2 = 9