1){2/(x-y)+6/(x+y)=1.1
{4/(x-y)-9/(x+y)= 0.1
сделаем замену
x+y=a
x-y=b
{2/b + 6/a= 1.1
{4/b-9/a=0.1
{2a+6b=1.1ab
{4a-9b=0.1ab
{2a+6b=ab+0.1ab
{4a-9b=0.1ab
{2a+6b=ab+4a-9b
{2a-15b+ab=0
{ab+2a=15b
{a(b+2)=15b
{a=15b/(b+2)
{Ставим
{60b/(b+2)-9b=0.1(15b/(b+2))b
{b=4
{a=10
тогда
x+y=a
x-y=b
{x+y=10
{x-y=4
{x=4+y
{4+2y=10
{2y=6
{y=3
{x=7
Ответ ( 7 ; 3)
2)
{1/x+1/y=3/2
{1/x^2+1/y^2=5/4
{(1/x+1/y)^2=9/4 в квадрат!
{1/x^2+1/y^2+2/xy=9/4
{2/xy=1
{xy=2
{y=2/x
{1/x+x/2=3/2
{2+x^2=3x
x1=1
x2=2
{y=2 y=1
Ответ ( 1 2) (2 1 )
3)
{ x+y=8
{x/y+y/x=50/7
x= 8-y
{8-y/y+y/(8-y) = 50/7
{7((8-y)^2+y^2)= 50(y(8-y))
{7(64-16y+2y^2) = 400y-50y^2
y=1
y=7
x=7
y=1
Ответ (7 1) (1 7)
4)
{1/x-1/y=1/36
{ xy^2-x^2y=324
{36(y-x)=xy
{xy(y-x)=324
{y-x=xy/36
{x^2y^2/36=324
{ xy=108
{y=108/x
{ Ставим
1/x-1/y=1/36 сюда
{1/x-x/108=1/36
x=9
x=-12
y=9
y=12
Ответ 9 9 -12 12