Question

方程组{█(x+y=a@xy=b)的两组解为{█(x1=a1@y1=b1) {█(x2=a2@y2=b2)┤ ┤ ┤ 求

Answer 1

y=a-x

x(a-x)=b

x^2-ax+b=0

由韦达定理知

x1x2=b,x1+x2=a

y1y2=(a-x1)(a-x2)=a^2-a(x1+x2)+x1x2=b

a1a2-b1b2=0