Решите уравнение: 5x^2+4x-1=0 3x^2+10x+7=0 16x^2-2x-5=0 -7x^2-4x+11=0 28x^2-36x+11=0 -23x^2-22x+1=0 -49x^2+21x-2=0 3x^2-14x+16=0

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1) 5x^2 + 4x - 1 = 0
Дискриминант D = 4^2 - 45(-1) = 16 + 20 = 36
x1 = (-4 + √36) / (25) = (-4 + 6) / 10 = 0.2
x2 = (-4 - √36) / (25) = (-4 - 6) / 10 = -1

Ответ: x1 = 0.2, x2 = -1

2) 3x^2 + 10x + 7 = 0
D = 10^2 - 437 = 100 - 84 = 16
x1 = (-10 + √16) / (23) = (-10 + 4) / 6 = -1
x2 = (-10 - √16) / (23) = (-10 - 4) / 6 = -2/3

Ответ: x1 = -1, x2 = -2/3

3) 16x^2 - 2x - 5 = 0
D = (-2)^2 - 416(-5) = 4 + 320 = 324
x1 = (2 + √324) / (216) = (2 + 18) / 32 = 20/32 = 5/8
x2 = (2 - √324) / (216) = (2 - 18) / 32 = -16/32 = -1/2

Ответ: x1 = 5/8, x2 = -1/2

4) -7x^2 - 4x + 11 = 0
D = (-4)^2 - 4(-7)11 = 16 + 308 = 324
x1 = (4 + √324) / (2(-7)) = (4 + 18) / (-14) = 22 / (-14) = -11/7
x2 = (4 - √324) / (2(-7)) = (4 - 18) / (-14) = -14 / (-14) = 1

Ответ: x1 = -11/7, x2 = 1

5) 28x^2 - 36x + 11 = 0
D = (-36)^2 - 42811 = 1296 - 1232 = 64
x1 = (36 + √64) / (228) = (36 + 8) / 56 = 44/56 = 11/14
x2 = (36 - √64) / (228) = (36 - 8) / 56 = 28/56 = 1/2

Ответ: x1 = 11/14, x2 = 1/2

6) -23x^2 - 22x + 1 = 0
D = (-22)^2 - 4(-23)1 = 484 + 92 = 576
x1 = (22 + √576) / (2(-23)) = (22 + 24) / (-46) = 46 / (-46) = -1
x2 = (22 - √576) / (2(-23)) = (22 - 24) / (-46) = -2 / (-46) = 1/23

Ответ: x1 = -1, x2 = 1/23

7) -49x^2 + 21x - 2 = 0
D = 21^2 - 4(-49)(-2) = 441 - 392 = 49
x1 = (-21 + √49) / (2(-49)) = (-21 + 7) / (-98) = -14 / (-98) = 1/7
x2 = (-21 - √49) / (2(-49)) = (-21 - 7) / (-98) = -28 / (-98) = 2/7

Ответ: x1 = 1/7, x2 = 2/7

8) 3x^2 - 14x + 16 = 0
D = (-14)^2 - 4316 = 196 - 192 = 4
x1 = (14 + √4) / (23) = (14 + 2) / 6 = 16/6 = 8/3
x2 = (14 - √4) / (23) = (14 - 2) / 6 = 12/6 = 2

Ответ: x1 = 8/3, x2 = 2