X^2-13x+40=0 x^2-6x-27=0 x^2+11x+18=0 5x^2-37x+60=0 9x^2-6x-8=0 решить через дискременант

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1) x^2 - 13x + 40 = 0

D = (-13)^2 - 4140 = 169 - 160 = 9

x1 = (13 + √9) / 2 = (13 + 3) / 2 = 16 / 2 = 8
x2 = (13 - √9) / 2 = (13 - 3) / 2 = 10 / 2 = 5

Ответ: x1 = 8, x2 = 5

2) x^2 - 6x - 27 = 0

D = (-6)^2 - 41(-27) = 36 + 108 = 144

x1 = (6 + √144) / 2 = (6 + 12) / 2 = 18 / 2 = 9
x2 = (6 - √144) / 2 = (6 - 12) / 2 = -6 / 2 = -3

Ответ: x1 = 9, x2 = -3

3) x^2 + 11x + 18 = 0

D = 11^2 - 4118 = 121 - 72 = 49

x1 = (-11 + √49) / 2 = (-11 + 7) / 2 = -4 / 2 = -2
x2 = (-11 - √49) / 2 = (-11 - 7) / 2 = -18 / 2 = -9

Ответ: x1 = -2, x2 = -9

4) 5x^2 - 37x + 60 = 0

D = (-37)^2 - 4560 = 1369 - 240 = 1129

x1 = (37 + √1129) / 10 = (37 + 33.6) / 10 = 70 / 10 = 7
x2 = (37 - √1129) / 10 = (37 - 33.6) / 10 = 3.4 / 10 = 0.34

Ответ: x1 ≈ 7, x2 ≈ 0.34

5) 9x^2 - 6x - 8 = 0

D = (-6)^2 - 49(-8) = 36 + 288 = 324

x1 = (6 + √324) / 18 = (6 + 18) / 18 = 24 / 18 = 4/3
x2 = (6 - √324) / 18 = (6 - 18) / 18 = -12 / 18 = -2/3

Ответ: x1 = 4/3, x2 = -2/3