Объяснение:= b2 - 4ac = 92 - 4·2·10 = 81 - 80 = 1
x1 = -9 - √1 2·2 = -9 - 1 4 = -10 4 = -2.5
x2 = -9 + √1 2·2 = -9 + 1 4 = -8 4 = -2
D = b2 - 4ac = 172 - 4·1·0 = 289 - 0 = 289
x1 = -17 - √289 2·1 = -17 - 17 2 = -34 2 = -17
x2 = -17 + √289 2·1 = -17 + 17 2 = 0 2 = 0
D = b2 - 4ac = 82 - 4·5·(-4) = 64 + 80 = 144
x1 = -8 - √144 2·5 = -8 - 12 10 = -20 10 = -2
x2 = -8 + √144 2·5 = -8 + 12 10 = 4 10 = 0.4
D = b2 - 4ac = (-2)2 - 4·7·(-14) = 4 + 392 = 396
x1 = 2 - √396 2·7 = 1 7 - 3 7 √11 ≈ -1.2785534815808857
x2 = 2 + √396 2·7 = 1 7 + 3 7 √11 ≈ 1.5642677672951713
= b2 - 4ac = (-7)2 - 4·1·12 = 49 - 48 = 1
x1 = 7 - √1 2·1 = 7 - 1 2 = 6 2 = 3
x2 = 7 + √1 2·1 = 7 + 1 2 = 8 2 = 4
Объяснение:
Во-первых, область определения
-x^2 - 8x - 7 >= 0
x^2 + 8x + 7 <= 0
(x + 1)(x + 7) <= 0
x = [-7; -1]
Во-вторых, выделяем корень
√(-x^2 - 8x - 7) = -ax + 2a + 3
Возводим в квадрат
-x^2-8x-7 = (-ax+2a+3)^2 = a^2*x^2-4a^2*x+4a^2-6ax+12a+9
x^2*(a^2 + 1) + x*(8 - 4a^2 - 6a) + (7 + 4a^2 + 12a + 9) = 0
x^2*(a^2 + 1) + 2x*(-2a^2 - 3a + 4) + (4a^2 + 12a + 16) = 0
Получили квадратное уравнение.
Если оно имеет только 1 корень, то D = 0
D/4 = (-2a^2 - 3a + 4)^2 - (a^2 + 1)(4a^2 + 12a + 16) =
= (4a^4 + 12a^3 + 9a^2 - 16a^2 - 24a + 16) -
- (4a^4 + 4a^2 + 12a^3 + 12a + 16a^2 + 16) =
= 9a^2 - 16a^2 - 24a - 4a^2 - 12a - 16a^2 = -27a^2 - 36a = -9a(3a + 4) = 0
a1 = 0; a2 = -4/3
Подставляем эти а и проверяем х.
1) a = 0
0 + √(-x^2 - 8x - 7) = 3
-x^2 - 8x - 7 = 9
-x^2 - 8x - 16 = -(x + 4)^2 = 0
x1 = x2 = -4
2) a = -4/3
-4x/3 + √(-x^2 - 8x - 7) = -8/3 + 3 = 1/3
√(-x^2 - 8x - 7) = 4x/3 + 1/3 = (4x + 1)/3
9(-x^2 - 8x - 7) = (4x + 1)^2
-9x^2 - 72x - 63 = 16x^2 + 8x + 1
25x^2 + 80x + 64 = (5x + 8)^2 = 0
x1 = x2 = -8/5