4.) 1) х^2-у^2=18, (х-у)(х+у)=18,
х+у=9, => (х-у)*9=18, х-у=2, х=2+у, =>
2+у+у=9, 2у=9-2=7, у=3,5,
х=2+3,5=5,5;
3) х-у=7; х^2-у^2=56, (х-у)(х+у)=56;
7*(х+у)=56, х+у=8;
7+у+у=8, 2у=8-7=1, у=1/2=0,5;
х=7+0,5=7,5;
5.) 1) у(у+х)=4, у+х=4/у;
х(х+у)=-3, х*4/у=-3 |*у, 4х=-3у, х=-3/4*у;
у(у-3/4*у)=4, у*1/4у=4 |*4, у^2=16,
извлекаем корень у=+-4;
а) у=4, х=-3/4*4=-3, (-3;4)
б) у=-4, х=-3/4*(-4)=3, (3; -4)
3) х=7+у, х^2+2ху+у^2=9, (х+у)^2=9;
(7+у+у)^2=9, (7+2у)^2=9, 49+28у+4у^2-9=0,
4у^2+28у+40=0 |:4, у^2+7у+10=0,
у^2+2у+5у+10=0, у(у+2)+5(у+2)=0,
(у+2)(у+5)=0; у1=-2, у2=-5;
а) у=-2, х=7-2=5 (5; -2);
б) у=-5, х=7-5=2 (2; -5)
6.) х^3-у^3=9, (х-у)(х^2+ху+у^2)=9;
х-у=3, => 3*(х^2+ху+у^2)=9 |:3;
х=3+у, => (3+у)^2+(3+у)у+у^2=3,
9+6у+у^2+3у+у^2+у^2=3,
9+9у+3у^2=3 |:3, у^2+3у+3-1=0,
у^2+2у+у+2=0, у(у+2)+(у+2)=0,
(у+2)(у+1)=0, у1=-2, у2=-1;
а) у=-2, х=3-2=1; (1; -2);
б) у=-1, х=3-1=2; (2; -1).