Odpowiedź:
a)
(1/9)x² - (1 1/3)x = - 2
(1/9)x² - (4/3)x + 2 = 0 | * 9
x²- 12x +18 = 0
a= 1 , b = - 12 , c = 18
Δ = b² - 4ac = (-12)² - 4 * 1 * 18 = 144 - 72 = 72
√Δ = √72 = √(36 * 2) = 6√2
x₁ = ( - b - √Δ)/2a = ( 12 - 6√2)/2 = 6(2 - √2)/2 = 3(2 - √2)
x₂ = (- b + √Δ)/2a = (12 + 6√2)/2 = 6(6 + √2)/2 = 3(2 + √2)
b)
(2x - 3)² = 8x
4x² - 12x + 9 - 8x = 0
4x² - 20x + 9 = 0
a = 4 , b = - 20 , c = 9
Δ = b² - 4ac = (-20)² - 4 * 4 * 9 = 400 - 324 = 76
√Δ = √76 = √(4 * 19) = 2√19
x₁ = ( - b - √Δ)/2a = ( 20 - 2√19)/8 = 2(10 - √19)/8 = (10 - √19)/4
x₂ = (- b + √Δ)/2a = (20 + 2√149)/8 = 2(10+ √19)/8 = (10 + √19)/4
c)
(x - 1)(x - 2) = 20
x² - x - 2x + 2 - 20 = 0
x² - 3x - 18 = 0
a = 1 , b = - 3 , c = - 18
Δ = b² - 4ac = (- 3)² - 4 * 1 * ( - 18) = 9 + 72 = 81
√Δ = √81 = 9
x₁ = ( - b - √Δ)/2a = ( 3 - 9)/2= - 6/2 = - 3
x₂ = (- b + √Δ)/2a = (3 + 9)/2 = 12/2 = 6
d)
(2/9)x² + (7/30)x = 1,3 | * 90
20x² + 21x = 117
20x²+ 21x - 117 = 0
a = 20 , b = 21 , c = - 117
Δ = b² - 4ac = 21² - 4 * 20 * (- 117) = 441 + 9360 = 9801
√Δ = √9801 = 99
x₁ = ( - b - √Δ)/2a = ( -21 - 99)/40= - 120/40 = - 3
x₂ = (- b + √Δ)/2a = (- 21 + 99)/40 = -78/40= - 1 38/40 = - 1 19/20
