已知3x-2y-5z=0,2x-5y+4z=0,且x,y,z均不等于0,求3x^2+2y^2+5z^2/5x^2+y^2-9z^2
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已知3x-2y-5z=0,2x-5y+4z=0,且x,y,z均不等于0,求3x^2+2y^2+5z^2/5x^2+y^2-9z^2
已知3x-2y-5z=0,2x-5y+4z=0,且x,y,z均不等于0,求3x^2+2y^2+5z^2/
5x^2+y^2-9z^2
已知3x-2y-5z=0,2x-5y+4z=0,且x,y,z均不等于0,求3x^2+2y^2+5z^2/5x^2+y^2-9z^2
【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
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