代数变换问题已知实数a、b、c,且.若实数b≠0,且x1,x2,y1,y2满足x1^2+ax2^2=bx2y1-x1y2=ax1y_数学解答

代数变换问题
已知实数a、b、c,且.
若实数b≠0,且x1,x2,y1,y2满足
x1^2+ax2^2=b
x2y1-x1y2=a
x1y1+ax2y2=c
则y1^2+ay2^2的值为

人气：330 ℃　时间：2020-10-01 09:47:14

解答

x2y1-x1y2=a(x2y1-x1y2)^2=a^2x2^2y1^2+x1^2y2^2-2x1x2y1y2=a^2ax2^2y1^2+ax1^2y2^2-2ax1x2y1y2=a^3①x1y1+ax2y2=c(x1y1+ax2y2)^2=c^2x1^2y1^2+a^2x2^2y2^2+2ax1x2y1y2=c^2②①+②x1^2y1^2+a^2x2^2y2^2+ax1^2y2^2+ax...