Question

若X1,X2是方程2X^2-6X+3=0的两个实数根,不解方程,求下列式子

（1）X1^2+X2^2
（2）2010/X1-2010/X2

Answer 1

X1+X2=-b/a=3
X1*X2=c/a=3/2
X1^2+X2^2 =(X1+X2)^2-2X1X2=9-3=6

(x1-x2)^2=x1^2+x2^2-2x1*x2=6-3=3
∴ x2-x1=+-根号3

2010/X1-2010/X2=2010*(1/x1-1/x2)=2010*(x2-x1)/x1*x2=±2010*√3*2/3=±1340√3

Answer 2

X1,X2是方程2X^2-6X+3=0的两个实数根
所以X1+X2=3，X1X2=1.5
(1)X1^2+X2^2=（X1+X2）^2-2X1X2=9-3=6
(2)2010/X1-2010/X2=2010(X2-X1)/X1X2
=1340(X2-X1)
(X2-X1)=正负根号(（X1+X2）^2-4X1X2)=正负根号3
2010/X1-2010/X2=1340根号3或-1340根号3

Answer 3

X1^2+X2^2
=(X1+X2)^2-2X1X2
=9-3
=6

2010/X1-2010/X2
=2010(X1-X2)/(X1X2)
=±2010√[(X1+X2)^2-4X1X2]/(X1X2)
=±1340√3