已知一元二次方程2X²+3x-1=0的两个根为X1,X2,求下列各式的值1) (X1+1)(X2+1)2) X1/1+X2/13) X²1+X²2
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![已知一元二次方程2X²+3x-1=0的两个根为X1,X2,求下列各式的值1) (X1+1)(X2+1)2) X1/1+X2/13) X²1+X²2](/uploads/image/z/996846-6-6.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8B2X%26%23178%3B%2B3x-1%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%E4%B8%BAX1%2CX2%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC1%EF%BC%89+%EF%BC%88X1%2B1%EF%BC%89%EF%BC%88X2%2B1%EF%BC%892%EF%BC%89+X1%2F1%2BX2%2F13%EF%BC%89+X%26%23178%3B1%2BX%26%23178%3B2)
已知一元二次方程2X²+3x-1=0的两个根为X1,X2,求下列各式的值1) (X1+1)(X2+1)2) X1/1+X2/13) X²1+X²2
已知一元二次方程2X²+3x-1=0的两个根为X1,X2,求下列各式的值
1) (X1+1)(X2+1)
2) X1/1+X2/1
3) X²1+X²2
已知一元二次方程2X²+3x-1=0的两个根为X1,X2,求下列各式的值1) (X1+1)(X2+1)2) X1/1+X2/13) X²1+X²2
x1+x2=-3/2, x1x2=-1/2
1)(x1+1)(x2+1)=x1x2+(x1+x2)+1=-1/2-3/2+1=-1
2)1/x1+1/x2=(x1+x2)/(x1x2)=-3/(-1)=3
3)x1^2+x2^2=(x1+x2)^2-2x1x2=9/4+1=13/4
利用x1+x2各x1*x2的值化简后求
韦达定理:X1+X2=-b/a =-3/2 X1.X2=c/a=-1/2
(1)=X1X2+(X1+X2)+1=-1/2+(-3/2)+1=-1
(2)=X1X2/X1+X2=-1/2/-3/2 =1/3
(3)=(X1+X2)的平方-2X1X2=-3/2的平方-2.(-1/2)=13/4