5.设x-1/x=3,求x十次方+x八次方+x平方+1/x十次方+x六次方+x四次方+1的值
问题描述:
5.设x-1/x=3,求x十次方+x八次方+x平方+1/x十次方+x六次方+x四次方+1的值
答
已知:x-1/x=3,求:(x^10+x^8+x^+1)/(x^10+x^6+x^4+1)的值 x-1/x=3(x-1/x)^2=x^2+1/x^2-2=9x^2+1/x^2=11 (x+1/x)^2=x^+2+1/x^2=13x+1/x=t,则t^2=13 x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=(x+1/x)[(x^2+2+1/x^2)-3]=(x+1/x...