已知3x-2y-5z=0,2x-5y+4z=0,且x,y,z均不为0,求3x*x+2y*y+5z*z/5x*x+y*y-9z*z的值.

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已知3x-2y-5z=0,2x-5y+4z=0,且x,y,z均不为0,求3x*x+2y*y+5z*z/5x*x+y*y-9z*z的值.
已知3x-2y-5z=0,2x-5y+4z=0,且x,y,z均不为0,求3x*x+2y*y+5z*z/5x*x+y*y-9z*z的值.

已知3x-2y-5z=0,2x-5y+4z=0,且x,y,z均不为0,求3x*x+2y*y+5z*z/5x*x+y*y-9z*z的值.
【解】
视z为常数,由已知两方程,可解得
x=3z
y=2z
将其代入待求值式中,得
3x*x+2y*y+5z*z/5x*x+y*y-9z*z
=[3(3z)^2+2(2z)^2+5z^2]/[5(3z)^2+(2z)^2-9z^2]
=40z^2/40z^2
=1

2x+3y* 6x-4y-5y*

视z为常数，由已知两方程，可解得
x=3z ，
y=2z
将其代入3x*x+2y*y+5z*z/5x*x+y*y-9z*z中，
得
3*(3z)*(3z)+2*(2z)*(2z)+5z*z/5*(3z)*(3z)+(2z)*(2z)-9z*z
=40z*z/40z*z
=1

解:
由3x-2y-5z=0,2x-5y+4z=0得
y=2z x=3z
原式=(3*3z*3z+2*2z*2z+5*z*z)/(5*3z*3z+2z*2z-9*z*z)
=(27+8+5)/(45+4-9)
=40/40=1

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