初中数学题.正数x1,x2,x3,x4,x5,x6同时满足x1/(x2x3x4x5x6)=1,x2/(x1x3x4x5x6)=2,x3/(x1x2x4x5x6)=3,x4/(x1x2x3x5x6)=4,x5/(x1x2x3x4x6)=6,x6/(x1x2x3x4x5)=9,求x1+x2+x3+x4+x5+x6

Question

初中数学题
.正数x1,x2,x3,x4,x5,x6同时满足x1/(x2x3x4x5x6)=1,x2/(x1x3x4x5x6)=2,x3/(x1x2x4x5x6)=3,x4/(x1x2x3x5x6)=4,x5/(x1x2x3x4x6)=6,x6/(x1x2x3x4x5)=9,求x1+x2+x3+x4+x5+x6

Answer 1

将x1/(x2x3x4x5x6)=1,x2/(x1x3x4x5x6)=2,x3/(x1x2x4x5x6)=3,x4/(x1x2x3x5x6)=4,x5/(x1x2x3x4x6)=6,x6/(x1x2x3x4x5)=9分别设为a,b,c,d,e,f式,令z为x1x2x3x4x5x6,
则将六个式子相乘可得到1/(z^4)=6^4(其中x^y表示x的y次方),
所以1/z=6,即1/（x1x2x3x4x5x6）=6,将其设为g式,
则当联立a式和g式,可得x1^2=1/6,
当联立b式和g式,可得x2^2=1/3,
同理可得,x3^2=1/2,
x4^2=2/3,
x5^2=1,
x6^2=3/2,
接下来开方求答案你会做啦