1
{x/y-y/x=8/3
{x²+y²=1000
x/y=t
t-1/t=8/3
3t²-8t-3=0
D=64+36=100
t1=(8-10)/6=-1/3⇒x/y=-1/3⇒y=-3x
x²+9x²=1000
10x²=1000
x²=100
x1=-10⇒y1=30 U x2=10⇒y2=-30
t2=(8+10)/6=3⇒x/y=3⇒x=3y
9y²+y²=1000
10y²=1000
y²=100⇒y3=-10⇒x3=-30 U y4=10⇒x4=30
Ответ (-10;30);(10;-30);(-30;-10);(30;10)
2
{1/(5x-6y)+x=2
{x/(5x-6y)=8
x=a,1/(5x-6y)=b
{a+b=2
{ab=-8
1)a=4,b=-2
x=4 U 1/(5x-6y)=-2
1/(20-6y)=-2⇒20-6y=-0,5⇒6y=20,5⇒y=3 5/12
2)a=-2,b=4
x=-2 U 1/(5x-6y=4⇒1/(-10-6y)=4⇒-10-6y=0,25⇒6y=-10,25⇒y=-1 17/24
(4;3 5/12);(-2;-1 17/24)
3
x=a,1/(4x-3y)=b
{a+b=2
{a*b=-24
1)a=6,b=-4
x=6 U 1/(4x-9y)=-4⇒1/(24-9y)=-4⇒24-9y=-1/4⇒9y=24 1/4⇒y=2 25/36
2)a=-4,b=6
x=-4 U 1/(4x-9y)=6⇒1/(-16-9y)=6⇒-16-9y=1/6⇒9y=-16 1/6⇒y=-2 25/36
(6;2 25/36);(-4;-2 25/36)