А) 3m^2 + 2m = 8
3m^2 + 2m - 8 = 0
a = 3, b = 2, c = -8
D = b^2 - 4ac = 4 - 4*3*(-8) = 4 + 96 = 100
m1 = (-b + sqrt(D))/2a = (-2+10)/2*3 = 8/6 = 4/3
m2 = (-b - sqrt(D))/2a = (-2-10)/2*3 = -12/6 = -2
Ответ: -2; 4/3.
б) x^2+12x=-35
x^2+12x+35=0
a=1, b=12, c=35
D = b^2 - 4ac = 144 - 4*1*35 = 144 - 140 = 4
x1 = (-b + sqrt(D))/2a = (-12+2)/2*1 = -10/2 = -5
x2 = (-b - sqrt(D))/2a = (-12-2)/2*1 = -14/2 = -7
Ответ: -7; -5.
в) 5y^2-8y+2=-1
5y^2-8y+2+1=0
5y^2-8y+3=0
a=5, b=-8, c=3
D = b^2 - 4ac = 64 - 4*5*3 = 64 - 60 = 4
y1 = (-b + sqrt(D))/2a = (-(-8)+2)/2*5 = 10/10 = 1
y2 = (-b - sqrt(D))/2a = (-(-8)-2)/2*5 = 6/10 = 3/5
Ответ: 3/5; 1.
г) 4m^2-2m-3=2
4m^2-2m-3-2=0
4m^2-2m-5=0
a=4, b=-2, c=-5
D = b^2 - 4ac = 4 - 4*4*(-5) = 84
m1 = (-b + sqrt(D))/2a = ((-2) + sqrt(84))/2*4 = (2+sqrt(4*21))/8 = (2+2sqrt(21))/8 = 2*(1+sqrt21)/8 = (1+sqrt(21))/4
m2 = (-b - sqrt(D))/2a = ((-2) - sqrt(84))/2*4 = (2-sqrt(4*21))/8 = (2-2sqrt(21))/8 = 2*(1-sqrt21)/8 = (1 - sqrt(21))/4