x^2+1/x^2=(x+1/x)^2-2=2x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=2x^4+1/x^4=(x^2+1/x^2)^2-2=2猜想x^n+1/x^n（n为自然数）的值 为 2 证明：（数学归纳法）设n=k时成立,即a^k+1/a^k=2,a^(k-1)+1/a^(k-1)]=2a^(k+1)+1/a^(k+1...