用换元法解方程x^2+1/(x^2)-9/2(x+1/x)+7=0,所设的辅助未知数y=?则原方程化为?
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用换元法解方程x^2+1/(x^2)-9/2(x+1/x)+7=0,所设的辅助未知数y=?则原方程化为?
用换元法解方程x^2+1/(x^2)-9/2(x+1/x)+7=0,所设的辅助未知数y=?则原方程化为?
用换元法解方程x^2+1/(x^2)-9/2(x+1/x)+7=0,所设的辅助未知数y=?则原方程化为?
x^2+1/(x^2)-9/2*(x+1/x)+7=0
(x+1/x)^2 -2 -9/2*(x+1/x)+7=0
(x+1/x)^2 -9/2*(x+1/x)+5=0
令y=x+1/x
则
y^2 -9/2*y+5=0
2y^2-9y+10=0
解得y=2 或y=5/2
代入 y=x+1/x
x+1/x=2
x^2-2x+1=0
(x-1)^2=0
x=1
x+1/x=5/2
2x^2-5x+1=0
x=(5+√17)/4
x=(5-√17)/4
y=1+1/x
y^2-9/2y+5=0
令,X+1/X=Y,
(X^2+1/X^2+2)-9/2(X+1/X)+5=0,
Y^2-9/2Y+5=0,
2Y^2-9Y+10=0,
Y1=5/2,Y2=2.
X+1/X=5/2,或X+1/X=2(方程无解,不合,舍去)
X1=1/2,X2=2,