巧解方程组

(X1)^2/6+(Y1)^2/2 = 1 ..........(1)λ^2(X2)^2/6+λ^2(Y2)^2/2 = λ^2..........(2)(1)-(2)=(X1+λX2)(X1-λX2）/6+(Y1+λY2)(Y1-λY2)/2=1-λ^2...(3)X1=λX2+3-3λ,X1-λX2=3(1-λ),Y1-λY2=0(3)变为:(2λX2+3-3λ)*3(1-λ)/6=1-λ^2=(1+λ)(1-λ)(2λX2+3-3λ)/2=1+λ得X2=(5λ-1)/(2λ) 收起

X1-3 = λ(X2-3） ...(1)Y1 = λY2 ...(2)(X1)^2/6+(Y1)^2/2 = 1 ==>(Y1)^2/2 =1 -(X1)^2/6 ...(3)(X2)^2/6+(Y2)^2/2 = 1 ==>(Y2)^2/2 =1 -(X2)^2/6 ...(4)(3)/(4) ==>(Y1/Y2)^2/2 =[1-(X1)^2/6]/[1 -(X2)^2/6] ...(5)(1)(2)代入(5), 即可解得: X2 =(5λ-1)/(2λ) 收起