已知：x^2 / (x^4+x^2+1)=1/4,计算(5x^4-3x^2+5) / 3x^2
问题描述：
已知：x^2 / (x^4+x^2+1)=1/4,计算(5x^4-3x^2+5) / 3x^2
答
由x^2/(x^4+x^2+1)=1/4可知:x^4+x^2+1=4x^2
将(5x^4-3x^2+5)/3x^2 化为：(5(x^4+x^2+1)-8x^2)/(3x^2)
=(5*4x^2-8x^2)/(3x^2)
=(12x^2)/(3x^2)
=4
答
x^2 / (x^4+x^2+1)=1/4
(x^4+x^2+1)/x^2=4
x^2+1+1/x^2=4
x^2+1/x^2=3
(5x^4-3x^2+5) / 3x^2
=(x^2+1/x^2)*5/3-1
=3*5/3-1
=4
答
x^2 / (x^4+x^2+1)=1/4
x^4+x^2+1=4x^2
x^4+1=3x^2
所以
(5x^4-3x^2+5) / 3x^2
=[5(x^4+1)-3x^2]/3x^2
=(5*3x^2-3x^2)/3x^2
=12x^2/3x^2
=4
答
真的好简单