Question

已知x2+y2 =7,xy=-2.求5x2 -3xy-4y2 -11xy-7x2 +2y2

Answer 1

x+y=7 xy=2

7^2=(x+y)^2=x^2+2xy+y^2=x^2+y^2+2*2

x^2+y^2=45

(1)y=7-x x(7-x)=2

x^2-7x+2=0

x=(7+41^(1/2))/2或x=(7-41^(1/2))/2

2x^2=(90+14*41^(1/2))/2,或=(90-14*41^(1/2))/2

(2) (x-y)^2=x^2-2xy+y^2=45-2*2=41