Question

已知X1.X2.Y1,Y2满足X1^2+5X2^2=10,X2Y1-X1Y2=5,X1Y1+5X2Y2=15求Y1^2+5Y2^2=?

Answer 1

按x1的2次方+5(x)的2次方=10 是x1的2次方+5(x2)的2次方=10 来算以x2y1-x1y2=5.........(1)x1y1+5x2y2=15.........(2)列方程组一,(1)*5x2+(2)*x1可得(5(x2)^2+(x1)^2)y1=25x2+15x110y1=25x2+15x1y1=(5x2+3x1)/2二,(2)*x2-(1)*x1可得(5(x2)^2+(x1)^2)y2=15x2-5x1y2=(3x2-x1)/2所以y1的2次方+5y2的2次方=(5x2+3x1)^2/4+5(3x2-x1)^2/4=[(25(x2)^2+30x1x2+9(x1)^2)+(45(x2)^2-5*6x1x2+5(x1)^2]/4=(70(x2)^2+14(x1)^2)/4=14(5(x2)^2+(x1)^2)/4=14*10/4=35

Answer 2

用消元法解出Y1=(5x2+3X1）/2，Y2=(3X2-X1)/2,然后，带入所求式中，得35