Question

решить систему уравнений:
а) у-2х=2, 5x^2 - y =1
б) х-2у^2=2, 3x+y=7

Answer 1

a) y=2+2-x
y=(4-x)
5x^2-4+x-1=0
5x^2+x-5=0
D=1^2-4*5*(-5)=1+100=101=√101
x1=(-1+√101)/2*5=(-1+10,05)/10=9,05/10
x1=0,905
x2=(-1-10,05)/10=(-11,05)/10
x2=-1,105
y1=(4-x1)=(4-0,905)
y1=3,095
y2=(4-x2)=(4-(-1,105))=4+1,105
y2=5,105

б) y=(7-3x)
x-2(7-3x)^2=2
x-2(49-42x+9x^2)=2
x-98+84x-18x^2=2
18x^2-85x+100=0
D=(-85)^2-4*18*100=7225-7200=25=5^2
x1=(-(-85)+5)/2*18=90/36
x1=2,5
x2=(-(-85)-5)/36=80/36
x2=20/9
y1=(7-3x1)=(7-3*2,5)=7-7,5
y1=-0,5
y2=(7-3x2)=7-3(20/9)=7-20/3=(21-20)/3
y2=1/3