Question

快！如果x1x2是一元二次方程ax2+bx+c=0的两根

如果x1x2是一元二次方程ax2+bx+c=0的两根 那么有x1+x2=-b/a，x1*x2=c/a
已知X1,X2是方程X²+6x+3=0的两个实数根，不解方程，求下列各式的值
(1) X1²+X2²
(2)1/X1+1/X2
(3)X2/X1+X1/X2

Answer 1

解：x1+x2=-b/a=-6 x1*x2=c/a=3

(1）
X1²+X2²
=（x1+x2)²-2(x1*x2)
=(-b/a)²-(2c/a)
=36-6
=30

(2)
1/X1+1/X2
=X2/(X1*X2）+X1/(X1*X2)
=X1+X2/X1*X2
=-6/3
=-2

(3)
X2/X1+X1/X2
=X2²/(X1*X2）+ X1²(/X1*X2）
=X1²+X2²/(X1*X2）
=30/3
=10

好歹也是我辛辛苦苦做的，辛辛苦苦打的
如果我做错了，请告诉我一声，谢谢

Answer 2

已知x1,x2是方程x²+6x+3=0的两个实数根，不解方程，求下列各式的值
x1+x2=-6
x1x2=3

(1) x1²+x2²=(x1+x2)²-2x1x2=30
(2)1/x1+1/x2=(x1+x2)/(x1x2)=-2
(3)x2/x1+x1/x2=(x1²+x2²)/(x1x2)=10

Answer 3

X1+X2=-6, X1*X2=3
(1)X1²+X2²=(X1+X2)²-2X1X2=36-6=30
(2)1/X1+1/X2=(X1+X2)/(X1*X2)=-6/3=-2
(3)X2/X1+X1/X2 =(X1²+X2²)/(X1*X2)=30/3=10

Answer 4

x1+x2=-6,x1x2=3
(1) X1²+X2²
=(x1+x2)^-2x1x2
=36-2*3=30
(2)1/X1+1/X2
=(x1+x2)/x1x2=-6/3=-2
(3)X2/X1+X1/X2
= (X1²+X2²)/x1x2=30/3=10