Using a suitable substitution , solve the equation
[(x^2)/(x+1)]+[(2x+2)/(x^2)]-3=0.
f.4 amaths
2007-01-02 8:00 am
回答 (1)
2007-01-02 8:05 am
✔ 最佳答案
[(x^2)/(x+1)]+[(2x+2)/(x^2)]-3=0. [(x^2)/(x+1)]+[2(x+1)/(x^2)]-3=0.
let y=[(x^2)/(x+1)]
then
we can transform the equation to
y+2/y-3=0
y^2-3y+2=0
(y-2)(y-1)=0
y=1 or 2
when y=1
(x^2)/(x+1)=1
x^2-x-1=0
x=1/2[1+ √5] or x=1/2[1- √5]
when y=2
(x^2)/(x+1)=2
x^2-2x-2=0
x=1/2[2+√12] or x=1/2[2-√12]
x=1+√3 or x=1-√3
收錄日期: 2021-04-25 16:52:17
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