设a,b,c,x,y,z是非零实数,且x/a+2b+c=y/a-c=z/a-2b+c,证明:a/x+2y+z=b/x-z=c/x-2y+z
人气:140 ℃ 时间:2020-06-11 06:57:51
解答
设x/(a+2b+c)=y/(a-c)=z/(a-2b+c) = k,(显然k≠0)则x = (a+2b+c)ky = (a-c)kz = (a-2b+c)k于是(直接代入),a/(x+2y+z) = a/(4ak) = 1/(4k)b/(x-z) = b/(4bk) = 1/(4k)c/(x-2y+z) = c/(4ck) = 1/(4k)综上所述,a/(x...
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