2. x^2-2xy-y^2=7
x-3y=5
x^2-2xy-y^2=7
x=5+3y
(5+3y)^2-2y(5+3y)-y^2=7
25+30y+9y^2-10y-6y^2-y^2=7
2y^2+20y+18=0 |:2
y^2+10y+9=0
D=100-26=64
y1=-10+8/2=-1
y2=-10-8/2=-9
при y=-1
x-3*(-1)=5
x=2
при y=-9
x-3*(-9)=5
x=-22
ответ: (2;1) (-22;-9)
1) (x+3)(y-2)=0
3x-2y=9
(x+3)(y-2)=0
x=9+2y/3
(9+2y/3+3)(y-2)=0 |*3
(9+2y+9)(3y-6)=0
(18+2y)(3y-6)=0
54y+108+6y^2-12y=0
6y^2+42y-108=0 |:6
y^2+7y-18=0
D=49+72=121
y1=-7+11/2=2
y2=-7-11/2=-9
при y=-9
3x-2*(-9)=9
3x+18=9
3x=-9 |:3
x=-3
при y=2
3x-2*2=9
3x-4=9
3x=13
x=4*(1/3)
ОТВЕТ: (-3;-9); (4*(1/3);2)
t²+8t=m
m²+19m+84=0
D=19²-4*84=25
m=(-19+5)/2=-14/2=-7
m=(-19-5)/2=-24/2=-12
1) t²+8t=-7
t²+8t+7=0
a-b+c=0 (1-8+7=0) => t=-1, t=-7
2) t²+8t=-12
t²+8t+12=0
D=8²-4*12=16
t=(-8+4)/2=-2
t=(-8-4)/2=-6
ответ: t=-7, t=-6, t=-2, t=-1
2.
t²-9t=m
m²+22m+112=0
D=22²-4*112=36
m=(-22+6)/2=-8
m=(-22-6)/2=-14
1) t²-9t=-8
t²-9t+8=0
a+b+c=0 (1-9+8=0) => t=1, t=8
2) t²-9t=-14
t²-9t+14=0
D=9²-4*14=25
t=(9-5)/2=2
t=(9+5)/2=7
ответ: t=1, t=2, t=7, t=8