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/
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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
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/](/uploads/image/z/16386971-59-1.jpg?t=%E5%B7%B2%E7%9F%A53x-2y-5z%3D0%2C2x-5y%2B4z%3D0%2C%E4%B8%94x%2Cy%2Cz%E5%9D%87%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E6%B1%823x%5E2%2B2y%5E2%2B5z%5E2%2F)
【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
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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