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a)
x² = x
x² - x = 0
x(x - 1) = 0
x = 0 lub x = 1
b)
x² = - x
x² + x = 0
x(x + 1) = 0
x = 0 lub x = - 1
c)
121 - x² = 0
(11 - x)(11 + x) = 0
11 - x = 0 lub 11 + x = 0
x = 11 lub x = - 11
d)
9x² - 49 = 0
(3x - 7)(3x + 7) = 0
3x - 7 = 0 lub 3x + 7 = 0
x = 7/3 lub x = - 7/3
x = 2 1/3 lub x = - 2 1/3
e)
36x² + 12x + 1 = 0
Δ = 12² - 4 * 36 * 1 = 144 - 144 = 0
x₁ = x₂ = - b/2a = - 12/72 = - 1/6
f)
25x² - 40x + 16 = 0
Δ = (- 40)² - 4 * 25 * 16 = 1600 - 1600 = 0
x₁ = x₂ = - b/2a = 40/50 = 8/5 = 1 3/5