分类：教育/科学-理工学科-数学
问题：八年级数学已知X/(X^2
已知X/(X^2-X+1)=7
求:X^2/(X^4+X^2+1)的值
回答：已知X/(X^2-X+1)=7
求:X^2/(X^4+X^2+1)的值

解 ∵ x/(x^2-x+1)=7
∴ x=7(x^2-x+1)            (1)
∴15x=7(x^2+x+1)           (2)
(1)两边平方得:
x^2=49(x^4-2x^3+3x^2-2x+1)        (3)
(2)两边平方得:
225x^2=49(x^4+2x^3+3x^2+2x+1)     (4)

(3)+(4)得:
226x^2=98(x^4+3x^2+1)             (5)

(5)<==>
15x^2=49(x^4+x^2+1)
∴x^2/(x^4+x^2+1)=49/15