Question

已知实数a,b,c两两不相等,且a+1÷b=b+1÷c=c+1÷a 求a2b2c2的值

Answer 1

a+1÷b=b+1÷c=c+1÷a

a+1/a=b+1/b;

a-b=1/b-1/a

a-b=(a-b)/(ab);

因为a,b不相等,因此,a-b不为0.两边同时除a-b;

有ab=1;

同理有bc=1;ac=1

a^2*b^2*c^2

=(ab)*(bc)*(ac)

=1