Question

a,b,c,d是互不相等的整数,a+1/b=b+1/c=c+1/d=d+1/a=x.求x得值.3Q

Answer 1

=1/(x-a) ,代入 b+1/c =x 得：c=(x-a)/(x^2-ax-1) 代入c+1/d=x 得 (x-a)/(x^2-ax-1) +1/d =x 整理得 dx^3-(ad+1)x^2+(a-2d)x+(ad+1)=0 由d+ 1/a=x,所以 ad+1=ax 所以 (d-a)x^3+(a-2d)x+ax=0 所以(d-a)x^3+2(a-d)x=0 因为a≠d 所以 x^3-2x=0 所以x = 0 或√2 或 -√2 当x=0时,ab=bc=cd=ad=-1 则有 a=c,b=d,与题意不符 综上所述,x = ±√2