若x为x²-2x-2=0的正整数根,求(x²-1)/(x²+x)÷[x-(2x-1)/x]
问题描述：
若x为x²-2x-2=0的正整数根,求(x²-1)/(x²+x)÷[x-(2x-1)/x]
答
(x²-1)/(x²+x)÷[x-(2x-1)/x]=(x+1)(x-1)/x(x+1)÷[(x²-2x+1)/x]=(x-1)/x÷[(x-1)²/x]=1/(x-1)x为x²-2x-2=0的正整数根,x-1≥0x²-2x+1-3=0x²-2x+1=3(x-1)²=3x-1=√3原式=1/(...