Question

已知x+1/x=3, 求x方/x四次方+x方+1的值

Answer 1

如果能求出（x四次方+x方+1）/x方也行，而且你可以发现（x四次方+x方+1）/x方=x²+1+1/x²，显然你会想到把x+1/x=3俩边平方，得x²+2+1/x²=9,即x²+1/x²=7，说明(x四次方+x方+1)/x方=x²+1+1/x²=8所以x方/x四次方+x方+1=1/8

Answer 2

因为x+1/x=3 两边平方
得 x^2+ 2 + 1/x^2=9
得 x^2+ 1/x^2=7
先求 （x^4+x^2+1）/x^2=x^2+1/x^2+1=8
所以 x^2/（x^4+x^2+1）=1/8

Answer 3

x方/x四次方+x方+1
=1/(x²+1+1/x²)
=1/(x²+2+1/x²-1)
=1/[(x+1/x)²-1]
=1/(3²-1)
=1/8

Answer 4

21/4