设X1,X2是方程3X^2+6x-2=0的两个根,利用根与系数的关系,求下列各式的值(1) (x1+1)(x2+1)(2) x1^2x2+x1x2^2 (3) 1/x1+1/x2(4) (x1-x2)^2
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![设X1,X2是方程3X^2+6x-2=0的两个根,利用根与系数的关系,求下列各式的值(1) (x1+1)(x2+1)(2) x1^2x2+x1x2^2 (3) 1/x1+1/x2(4) (x1-x2)^2](/uploads/image/z/6071942-38-2.jpg?t=%E8%AE%BEX1%2CX2%E6%98%AF%E6%96%B9%E7%A8%8B3X%5E2%2B6x-2%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%2C%E5%88%A9%E7%94%A8%E6%A0%B9%E4%B8%8E%E7%B3%BB%E6%95%B0%E7%9A%84%E5%85%B3%E7%B3%BB%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC%281%29+%28x1%2B1%29%28x2%2B1%29%282%29+x1%5E2x2%2Bx1x2%5E2+%283%29+1%2Fx1%2B1%2Fx2%284%29+%28x1-x2%29%5E2)
设X1,X2是方程3X^2+6x-2=0的两个根,利用根与系数的关系,求下列各式的值(1) (x1+1)(x2+1)(2) x1^2x2+x1x2^2 (3) 1/x1+1/x2(4) (x1-x2)^2
设X1,X2是方程3X^2+6x-2=0的两个根,利用根与系数的关系,求下列各式的值
(1) (x1+1)(x2+1)
(2) x1^2x2+x1x2^2
(3) 1/x1+1/x2
(4) (x1-x2)^2
设X1,X2是方程3X^2+6x-2=0的两个根,利用根与系数的关系,求下列各式的值(1) (x1+1)(x2+1)(2) x1^2x2+x1x2^2 (3) 1/x1+1/x2(4) (x1-x2)^2
方程的两根X1,X2和方程的系数a,b,c满足X1+X2=-(b/a),X1*X2=c/a (韦达定理).
1、X1X2+X1+X2+1=c/a-(b/a)+1=-2/3-2+1=-5/3.
2、x1x2(x1+x2)=4/3.
3、(X1+X2)/X1*X2=-b/c=3.
4、x1²-2x1x2+x2²=(x1+x2)²-4x1x2=20/3.
x1+x2=-6/3=-2
x1x2=-2/3
(1)(x1+1)(x2+1)=x1x2+(x1+x2)+1=-5/3
(2)x1^2x2+x1x2^2=x1x2(x1+x2)=4/3
(3)1/x1+1/x2=(x1+x2)/(x1x2)=3
(4)(x1-x2)^2=(x1+x2)^2-4x1x2=20/3