(x+y)/3=(y+z)/5=(z+x)/4 ,xyz不等于0,求x:y:z
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(x+y)/3=(y+z)/5=(z+x)/4 ,xyz不等于0,求x:y:z
(x+y)/3=(y+z)/5=(z+x)/4 ,xyz不等于0,求x:y:z
(x+y)/3=(y+z)/5=(z+x)/4 ,xyz不等于0,求x:y:z
令(x+y)/3=(y+z)/5+(z+x)/4=k
所以x+y=3k (1)
y+z=5k (2)
z+x=4k (3)
相加
2(x+y+z)=12k
x+y+z=6k (4)
用(4)分别减去(1)(2)(3)
z=3k,x=k,y=2k
所以x:y:z=1:2:3
设(x+y)/3=(y+z)/5=(z+x)/4=k
x+y=3k............1
y+z=5k.............2
z+x=4k.............3
以上3式相加得
2(x+y+z)=12k
x+y+z=6k...............4
将1式代入4式得
3k+z=6k
z=3k
将2式...
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设(x+y)/3=(y+z)/5=(z+x)/4=k
x+y=3k............1
y+z=5k.............2
z+x=4k.............3
以上3式相加得
2(x+y+z)=12k
x+y+z=6k...............4
将1式代入4式得
3k+z=6k
z=3k
将2式代入4式得
5k+x=6k
x=k
将3式代入4式得
4k+y=6k
y=2k
x:y:z
=k:2k:3k
=1:2:3
收起
1:2:3.
5(x+y=3(y+z))即5x+2y=3z ①
4(x+y)=3(x+z)即x+4y=3z ②
①-②得,2x=y;
①*2-②得,3x=z;
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