Odpowiedź:
1.
25x² - 81 = 0
zastosowany wzór skróconego mnożenia
a² - b² =(a - b)(a + b)
25x² - 81 =0
(5x - 9)(5x + 9) = 0
5x - 9 = 0 ∨ 5x + 9 =0
5x = 9 ∨ 5x = - 9
x = 9/5 ∨ x = - 9/5
x = 1 4/5 ∨ x = - 1 4/5
2.
x² - 8x + 15 =0
a = 1 , b = - 8 , c = 15
Δ = b² - 4ac = (- 8)² - 4 * 1 * 15 = 64 - 60 = 4
√Δ = √4 = 2
x₁ = ( - b - √Δ)/2a = (8 - 2)/2= 6/2 = 3
x₂ = (- b + √Δ)/2a = (8 + 2)/2 = 10/2 = 5
3.
5x² + 2x - 3 = 0
a = 5, b = 2 , c = - 3
Δ = b² - 4ac = 2² - 4 * 5 * ( - 3) =4 + 60 = 64
√Δ = √64 = 8
x₁ = ( - b - √Δ)/2a = (- 2 - 8)/10 = - 10/10 = - 1
x₂ = (- b + √Δ)/2a = ( - 2 + 8)/10 = 6/10 = 3/5
1.
2x² + 5x = 0
x(2x + 5) = 0
x = 0 ∨ 2x + 5 = 0
x = 0 ∨ 2x = - 5
x =0 ∨ x = - 5/2 = - 2 1/2
2.
x² - 7x + 12 = 0
a = 1 , b = - 7 , c = 12
Δ = b² - 4ac = (- 7)² - 4 * 1 * 12 = 49 - 48 = 1
√Δ = √1 = 1
x₁ = ( - b - √Δ)/2a = (7 - 1)/2 = 6/2 = 3
x₂ = (- b + √Δ)/2a = (7 + 1)/2 = 8/2 = 4
3.
3x² - 7x + 2 = 0
a = 3 , b = - 7 , c = 2
Δ = b² - 4ac = (- 7)² - 4 * 3 * 2 = 49 - 24 = 25
√Δ = √25 = 5
x₁ = ( - b - √Δ)/2a = (7 - 5)/6 = 2/6 = 1/3
x₂ = (- b + √Δ)/2a = (7 + 5)/6 = 12/6 = 2
