(1)已知a+b+c=6,a2+b2+c2=14,a3+b3+c3=36,求abc的值(2)(a-2b+c)(a+2b-c)-(a+2b+c)2(3)(x+y)4(x-y)4(4)(a+b+c)(a2+b2+c2-ab-ac-bc)(5)已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z)再加一道题:已知一个十边形中九个内
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![(1)已知a+b+c=6,a2+b2+c2=14,a3+b3+c3=36,求abc的值(2)(a-2b+c)(a+2b-c)-(a+2b+c)2(3)(x+y)4(x-y)4(4)(a+b+c)(a2+b2+c2-ab-ac-bc)(5)已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z)再加一道题:已知一个十边形中九个内](/uploads/image/z/374645-29-5.jpg?t=%EF%BC%881%EF%BC%89%E5%B7%B2%E7%9F%A5a%2Bb%2Bc%3D6%2Ca2%2Bb2%2Bc2%3D14%2Ca3%2Bb3%2Bc3%3D36%2C%E6%B1%82abc%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%EF%BC%88a-2b%2Bc%EF%BC%89%EF%BC%88a%2B2b-c%EF%BC%89-%EF%BC%88a%2B2b%2Bc%EF%BC%892%283%29%28x%2By%294%28x-y%294%284%29%28a%2Bb%2Bc%29%28a2%2Bb2%2Bc2-ab-ac-bc%29%285%29%E5%B7%B2%E7%9F%A5z2%3Dx2%2By2%2C%E5%8C%96%E7%AE%80%28x%2By%2Bz%29%28x-y%2Bz%29%28-x%2By%2Bz%29%28x%2By-z%29%E5%86%8D%E5%8A%A0%E4%B8%80%E9%81%93%E9%A2%98%EF%BC%9A%E5%B7%B2%E7%9F%A5%E4%B8%80%E4%B8%AA%E5%8D%81%E8%BE%B9%E5%BD%A2%E4%B8%AD%E4%B9%9D%E4%B8%AA%E5%86%85)
(1)已知a+b+c=6,a2+b2+c2=14,a3+b3+c3=36,求abc的值(2)(a-2b+c)(a+2b-c)-(a+2b+c)2(3)(x+y)4(x-y)4(4)(a+b+c)(a2+b2+c2-ab-ac-bc)(5)已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z)再加一道题:已知一个十边形中九个内
(1)已知a+b+c=6,a2+b2+c2=14,a3+b3+c3=36,求abc的值
(2)(a-2b+c)(a+2b-c)-(a+2b+c)2
(3)(x+y)4(x-y)4
(4)(a+b+c)(a2+b2+c2-ab-ac-bc)
(5)已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z)
再加一道题:已知一个十边形中九个内角的和的度数是1290度,那么这个十边形的另一个内角为多少度?
(1)已知a+b+c=6,a2+b2+c2=14,a3+b3+c3=36,求abc的值(2)(a-2b+c)(a+2b-c)-(a+2b+c)2(3)(x+y)4(x-y)4(4)(a+b+c)(a2+b2+c2-ab-ac-bc)(5)已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z)再加一道题:已知一个十边形中九个内
(1) (a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc=36
ab+ac+bc=11
(a+b+c)^3=a^3+b^3+c^3+6abc+3ab^2+3a^2b+3a^2c+3ac^2+3bc^2+3b^2c
=14+6abc+18(a^2+b^2+c^2)-3(a^3+b^3+c^3)=14+6abc+18*14-3*36=216
abc=29/3
(2)(a-2b+c)(a+2b-c)-(a+2b+c)2
=a^2-(2b-c)^2-(a^2+4b^2+c^2+4ab+2ac+4bc)
=a^2-4b^2+4bc-c^2-(a^2+4b^2+c^2+4ab+2ac+4bc)
=-8b^2-2c^2-4ab-2ac
(3)(x+y)4(x-y)4=(x^2-y^2)^4
(4)(a+b+c)(a2+b2+c2-ab-ac-bc)
=a^3+b^3+c^3-3abc
(5)(x+y+z)(x-y+z)(-x+y+z)(x+y-z)
=[(x+z)^2-y^2][y^2-(x-z)^2]
=[x^2+2xz+z^2-z^2+x^2][z^2-x^2-x^2-z^2+2xz]
=(2x^2+2xz)(-2x^2+2xz)
=2x(x+z)*(-2x)(x-z)
=-4x^2(x^2-z^2)
=4x^2y^2
你的这些题目写得不清楚,不好回答,到底是化简呢,还是求值?另外1和2中的a,b,c有没有关系?
(1) a,b,c值分别是1,2,3 abc=6
化简的时候有点问题,应该是ABC=6
a3+b3+c3+3(a2b+a2c+ab2+ac2+b2c+bc2)+6abc
=3a2(a+b+c)+3b2(a+b+c)+3c2(a+b+c)-2(a3+b3+c3)+6abc
=3*6(a2+b2+c2)-2*36+6abc
=18*14-2*36+6abc=6*6*6
6abc=216+72-252=36
abc=6
(1) (a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc=36
ab+ac+bc=11
(a+b+c)^3=a^3+b^3+c^3+6abc+3ab^2+3a^2b+3a^2c+3ac^2+3bc^2+3b^2c
=14+6abc+18(a^2+b^2+c^2)-3(a^3+b^3+c^3)=14+6abc+18*14-3*36=216
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(1) (a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc=36
ab+ac+bc=11
(a+b+c)^3=a^3+b^3+c^3+6abc+3ab^2+3a^2b+3a^2c+3ac^2+3bc^2+3b^2c
=14+6abc+18(a^2+b^2+c^2)-3(a^3+b^3+c^3)=14+6abc+18*14-3*36=216
abc=29/3
(2)(a-2b+c)(a+2b-c)-(a+2b+c)2
=a^2-(2b-c)^2-(a^2+4b^2+c^2+4ab+2ac+4bc)
=a^2-4b^2+4bc-c^2-(a^2+4b^2+c^2+4ab+2ac+4bc)
=-8b^2-2c^2-4ab-2ac
(3)(x+y)4(x-y)4=(x^2-y^2)^4
(4)(a+b+c)(a2+b2+c2-ab-ac-bc)
=a^3+b^3+c^3-3abc
(5)(x+y+z)(x-y+z)(-x+y+z)(x+y-z)
=[(x+z)^2-y^2][y^2-(x-z)^2]
=[x^2+2xz+z^2-z^2+x^2][z^2-x^2-x^2-z^2+2xz]
=(2x^2+2xz)(-2x^2+2xz)
=2x(x+z)*(-2x)(x-z)
=-4x^2(x^2-z^2)
=4x^2y^2
(6)多边形内角和为(n - 2)×180°
所以十边形内角和为1480°
1480-1290=190°
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