Задание:
1/x+1/y=5 1/x в квадрате +1/y в квадрате=13
Решение:
1/x+1/y=5, (x+y) /xy=5, x+y=5xy, 5xy-x=y, x (5y-1)=y, x=y/ (5y-1) , x^2=y^2/ (25y^2-10y+1).1/x^2+1/y^2=13, (x^2+y^2) /x^2y^2=13, x^2+y^2=13x^2y^2.y^2/ (25y^2-10y+1)+y^2=13y^4/ (25y^2-10y+1) , y^2*(25y^2-10y+1)+y^2=13y^4, 25y^4-10y^3+y^2+y^2=13y^4, 12y^4-10y^3+2y^2=0, 6y^2-5y+1=0, D=25-24=1, y1=(5-1) /12=1/3, y2=(5+1) /12=1/2.x1=(1/3) / (5/3-1)=(1/3) / (2/3)=1/2, x2=(1/2) / (5/2-1)=(1/2) / (3/2)=1/3.
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