4x^2-(4m+1)x+m^2-1=0不用解方程,题目(1)x1+x2(2)1/x1+1/x2(3)x1^2+x2^2(4)x1x2^2+x1^2x2(5)|x1-x2|(6)(x1+2)(x2+2)

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4x^2-(4m+1)x+m^2-1=0不用解方程,题目(1)x1+x2(2)1/x1+1/x2(3)x1^2+x2^2(4)x1x2^2+x1^2x2(5)|x1-x2|(6)(x1+2)(x2+2)
4x^2-(4m+1)x+m^2-1=0
不用解方程,题目(1)x1+x2(2)1/x1+1/x2(3)x1^2+x2^2(4)x1x2^2+x1^2x2
(5)|x1-x2|(6)(x1+2)(x2+2)

4x^2-(4m+1)x+m^2-1=0不用解方程,题目(1)x1+x2(2)1/x1+1/x2(3)x1^2+x2^2(4)x1x2^2+x1^2x2(5)|x1-x2|(6)(x1+2)(x2+2)
韦达定理
x1+x2=-b/a=(4m+1)/4
x1x2=c/a=(m²-1)/4
(1)x1+x2
x1+x2=(4m+1)/4
(2)1/x1+1/x2
1/x1+1/x2=(x1+x2)/(x1x2)=(4m+1)/(m²-1)
(3)x1²+x2²
x1²+x2²=(x1+x2)²-2x1x2=(4m+1)²/16-(m²-1)/2
(4)x1x2²+x1²x2
x1x2²+x1²x2=x1x2(x1+x2)=(4m+1)(m²-1)//16
(5)|x1-x2|
|x1-x2|=√(x1-x2)²=√[(x1+x2)²-4x1x2]
(6)(x1+2)(x2+2)
(x1+2)(x2+2)=x1x2+2(x1+x2)+4