given a,b,c are three points represent complex number in a complex plane
1.a^2+b^2+c^2=ab+bc+ca
2.a,b,c are equilateral triangle in complex plane
provew that
if a,b,c are the roots of x^3+3px^2+3qx+r=0,then p^2=q
complex1
2007-11-25 6:03 am
回答 (1)
2007-11-25 6:23 am
✔ 最佳答案
Using the relationships between roots and coefficientsa+b+c=-3p
ab+bc+ac=3q
So
(a+b+c)^2=9p^2
a^2+b^2+c^2+2ab+2bc+2ac=9p^2
3(ab+bc+ca)=9p^2
9q=9p^2
q=p^2
收錄日期: 2021-04-25 16:53:49
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