2x^2 - x - 1 = 0
a = 2, b = -1, c = -1
D = b^2 - 4ac = 1 - 4*2*(-1) = 9
x1 = (1 + 3)/2*2 = 4/4 = 1
x2 = (1 - 3)/2*2 = -2/4 = -1/2
Ответ: -1/2; 1.
2x^2 + x - 1 = 0
a = 2, b = 1, c = -1
D = b^2 - 4ac = 1 - 4*2*(-1) = 9
x1 = (-1 + 3)/2*2 = 2/4 = 1/2
x2 = (-1 - 3)/2*2 = -4/4 = -1
Ответ: -1; 1/2.
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1) S₁ = 4x * 3x = 12x² - площадь всего прямоугольника
2) S₂ = (3x - 1)(2x + 4) = 6x² + 12x - 2x - 4 = 6x² + 10x - 4 - площадь незакрашенного прямоугольника
3) S = S₁ - S₂ = 12x² - (6x² + 10x - 4) = 12x² - 6x² - 10x + 4 = 6x² - 10x + 4 - площадь закрашенного прямоугольника