若整数X Y Z满足(9/8)^X*(10/9)^Y*(16/15)^Z=2则x=__,y__,z=__.
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若整数X Y Z满足(9/8)^X*(10/9)^Y*(16/15)^Z=2则x=__,y__,z=__.
若整数X Y Z满足(9/8)^X*(10/9)^Y*(16/15)^Z=2则x=__,y__,z=__.
若整数X Y Z满足(9/8)^X*(10/9)^Y*(16/15)^Z=2则x=__,y__,z=__.
(9/8)^X*(10/9)^Y*(16/15)^Z=2
(3^x / 2^3x)*(2^y*5^y / 3^2y)*(2^4z/3^z *5^Z)=2,
3^(x-y-z)*2^(y+4z-3x)*5^(y-5z)=2,
X Y Z整数,所以:
x-y-z=0,
y+4z-3x=1,
y-5z=0
解方程组得:x=-2/3,y=-5/9,z=-1/9 .