若X1,X2是方程X^2+2X-2006=0的两根,求下列各式的值:(1)X1^2+X2^2 (2)(X1-5)(X2-5) (3)X1^3+X2^3 (4)|X1-X2|越详细越好,时间紧迫
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![若X1,X2是方程X^2+2X-2006=0的两根,求下列各式的值:(1)X1^2+X2^2 (2)(X1-5)(X2-5) (3)X1^3+X2^3 (4)|X1-X2|越详细越好,时间紧迫](/uploads/image/z/6924077-53-7.jpg?t=%E8%8B%A5X1%2CX2%E6%98%AF%E6%96%B9%E7%A8%8BX%5E2%2B2X-2006%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC%3A%281%29X1%5E2%2BX2%5E2+%282%29%28X1-5%29%28X2-5%29+%283%29X1%5E3%2BX2%5E3+%284%29%EF%BD%9CX1-X2%EF%BD%9C%E8%B6%8A%E8%AF%A6%E7%BB%86%E8%B6%8A%E5%A5%BD%2C%E6%97%B6%E9%97%B4%E7%B4%A7%E8%BF%AB)
若X1,X2是方程X^2+2X-2006=0的两根,求下列各式的值:(1)X1^2+X2^2 (2)(X1-5)(X2-5) (3)X1^3+X2^3 (4)|X1-X2|越详细越好,时间紧迫
若X1,X2是方程X^2+2X-2006=0的两根,求下列各式的值:
(1)X1^2+X2^2
(2)(X1-5)(X2-5)
(3)X1^3+X2^3
(4)|X1-X2|
越详细越好,时间紧迫
若X1,X2是方程X^2+2X-2006=0的两根,求下列各式的值:(1)X1^2+X2^2 (2)(X1-5)(X2-5) (3)X1^3+X2^3 (4)|X1-X2|越详细越好,时间紧迫
由韦达定理
x1+x2=-2,x1*x2=-2006
x1^2+x2^2=(x1+x2)^2-2x1*x2=4+2*2006=4016
(x1-5)(x2-5)
=x1*x2-5x1-5x2+25
=x1*x2-5(x1+x2)+25
=-2006+5*2+25
=-1971
x1^3+x2^3
=(x1+x2)(x1^2-x1x2+x2^2)
=-2*[4016-(-2006)]
=-12044
|x1-x2|
=√(x1-x2)^2
=√[(x1+x2)^2-4x1x2]
=√(4+4*2006)
=√8028
=6√223