若实数a,b,c,d满足 a /b = b/ c = c/ d = d/ a ,则 ab+bc+cd+da /(a^2+b^2+c^2+d^2)=
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若实数a,b,c,d满足 a /b = b/ c = c/ d = d/ a ,则 ab+bc+cd+da /(a^2+b^2+c^2+d^2)=
若实数a,b,c,d满足 a /b = b/ c = c/ d = d/ a ,则 ab+bc+cd+da /(a^2+b^2+c^2+d^2)=
若实数a,b,c,d满足 a /b = b/ c = c/ d = d/ a ,则 ab+bc+cd+da /(a^2+b^2+c^2+d^2)=
设a/b=b/c=c/d=d/a=k
a/b*b/c*c/d*d/a=1,故k*k*k*k=1,得k=1或-1.
k=1的情况,a=b=c=d,代入答案是1.
k=-1的情况,a=-b=c=-d,代入答案是-1.
所以答案是1或者-1.
令a/b=b/c=c/d=d/a=k
则ab/b^2=bc/c^2=cd/d^2=da/a^2=k
得ab=kb^2，bc=kc^2，cd=kd^2，da=ka^2
故(ab+bc+cd+da) /(a^2+b^2+c^2+d^2)
=(kb^2+kc^2+kd^2+ka^2)/(a^2+b^2+c^2+d^2)
=k=a /b = b/ c = ...
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令a/b=b/c=c/d=d/a=k
则ab/b^2=bc/c^2=cd/d^2=da/a^2=k
得ab=kb^2，bc=kc^2，cd=kd^2，da=ka^2
故(ab+bc+cd+da) /(a^2+b^2+c^2+d^2)
=(kb^2+kc^2+kd^2+ka^2)/(a^2+b^2+c^2+d^2)
=k=a /b = b/ c = c/ d = d/ a
答案：(ab+bc+cd+da) /(a^2+b^2+c^2+d^2)=a /b = b/ c = c/ d = d/ a
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简单点的，令a=b=c=d，可以满足上述条件
那么所求等于1