谢谢各位啦!还来了一个题目: 已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,谢谢各位啦!还来了一个题目:已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,求:arctan(x1)+arctan(x2)+arctan(x3)+arctan
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![谢谢各位啦!还来了一个题目: 已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,谢谢各位啦!还来了一个题目:已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,求:arctan(x1)+arctan(x2)+arctan(x3)+arctan](/uploads/image/z/5174446-22-6.jpg?t=%E8%B0%A2%E8%B0%A2%E5%90%84%E4%BD%8D%E5%95%A6%21%E8%BF%98%E6%9D%A5%E4%BA%86%E4%B8%80%E4%B8%AA%E9%A2%98%E7%9B%AE%EF%BC%9A+%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8B%EF%BC%9Ax%5E4%2Bax%5E3%2Bbx%5E2%2Bcx%2Bd%3D0%E7%9A%84%E5%9B%9B%E4%B8%AA%E6%A0%B9%E6%98%AFx1%2Cx2%2Cx3%2Cx4%2C%E8%B0%A2%E8%B0%A2%E5%90%84%E4%BD%8D%E5%95%A6%21%E8%BF%98%E6%9D%A5%E4%BA%86%E4%B8%80%E4%B8%AA%E9%A2%98%E7%9B%AE%EF%BC%9A%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8B%EF%BC%9Ax%5E4%2Bax%5E3%2Bbx%5E2%2Bcx%2Bd%3D0%E7%9A%84%E5%9B%9B%E4%B8%AA%E6%A0%B9%E6%98%AFx1%2Cx2%2Cx3%2Cx4%2C%E6%B1%82%EF%BC%9Aarctan%28x1%29%2Barctan%28x2%29%2Barctan%28x3%29%2Barctan)
谢谢各位啦!还来了一个题目: 已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,谢谢各位啦!还来了一个题目:已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,求:arctan(x1)+arctan(x2)+arctan(x3)+arctan
谢谢各位啦!还来了一个题目: 已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,
谢谢各位啦!还来了一个题目:
已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,求:
arctan(x1)+arctan(x2)+arctan(x3)+arctan(x4)=?
谢谢各位啦!还来了一个题目: 已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,谢谢各位啦!还来了一个题目:已知方程:x^4+ax^3+bx^2+cx+d=0的四个根是x1,x2,x3,x4,求:arctan(x1)+arctan(x2)+arctan(x3)+arctan
记y1=arctan(x1)+arctan(x2),有 tany1=(x1+x2)/(1-x1x2)
记y2=arctan(x3)+arctan(x4),有 tany2=(x3+x4)/(1-x3x4)
令y=arctan(x1)+arctan(x2)+arctan(x3)+arctan(x4)=y1+y2,
tany=(tany1+tany2)/(1-tany1tany2)
=[(x1+x2)/(1-x1x2)+(x3+x4)/(1-x3x4)]/[1-(x1+x2)(x3+x4)/(1-x1x2)(1-x3x4)]
=[(x1+x2)(1-x3x4)+(x3+x4)(1-x1x2)]/[(1-x1x2)(1-x3x4)-(x1+x2)(x3+x4)]
=[x1+x2+x3+x4-x1x3x4-x2x3x4-x1x2x3-x1x2x4]/[1-x1x2-x3x4+x1x2x3x4-x1x3-x1x4-x2x3-x2x4]
=[s1-s3]/[1-s2+s4]
这里s1=x1+x2+x3+x4,s2=x1x2+x1x3+x1x4+x2x3+x2x4+x3x4,s3=x1x2x3+x1x2x4+x1x3x4+x2x3x4
s4=x1x2x3x4
由韦达定理,有:s1=-a,s2=b,s3=-c,s4=d
因此y=(-a+c)/(1-b+d)
x3+x4=-c<0 (4) 有(1),(3)可知x1<0,x2<0,x3<0,x4<0首先看第一个方程,根=[-b加减√(b^2-4c)]/2,其中较大的根为 [-b