已知對于正數x有x^2+1/x^2=7 則x^5+1/x^5=?答案123
熱心網友
解答：由 x^2+1/x^2=7得：(x+1/x)^2=9x+1/x=3 或者 x+1/x=-3 (由題意，舍去）于是x^5+1/x^5=（x+1/x)(x^4-x^2+1-1/x^2+1/x^4)=3[(x^4+1/x^4)+1-(x^2+1/x^2)]=3[(x^2+1/x^2)^2-2+1-(x^2+1/x^2)]=3(49-2+1-7)=3*41=123
熱心網友
同樓上
已知對于正數x有x^2+1/x^2=7 則x^5+1/x^5=?答案123
解答：由 x^2+1/x^2=7得：(x+1/x)^2=9x+1/x=3 或者 x+1/x=-3 (由題意，舍去）于是x^5+1/x^5=（x+1/x)(x^4-x^2+1-1/x^2+1/x^4)=3[(x^4+1/x^4)+1-(x^2+1/x^2)]=3[(x^2+1/x^2)^2-2+1-(x^2+1/x^2)]=3(49-2+1-7)=3*41=123
同樓上