关于1\如果a、b、c是三角形ABC的边,请确定代数式a^2-b^2-c^2-2bc的值的符号.(写出过程)2\计算:(x+2y-3/2)(x-2y+3/2)3\计算:(x+3)(x^2+9)(x-3)

Question

关于
1\ 如果a、b、c是三角形ABC的边,请确定代数式a^2-b^2-c^2-2bc的值的符号.(写出过程)
2\ 计算:(x+2y-3/2)(x-2y+3/2)
3\ 计算:(x+3)(x^2+9)(x-3)

Answer 1

1 a^2-b^2-c^2-2bc
=a^2-(b^2+c^2+2bc)
=a^2-(b+c)^2
=(a+(b+c))(a-(b+c))
三角形,任何两边之和大于第三边,故b+c>a, 从而得知 a-(b+c)<0
而 (a+(b+c))>0
a^2-b^2-c^2-2bc<0
2 (x+2y-3/2)(x-2y+3/2)
=(x+(2y-3/2))(x-(2y-3/2))
=x^2-(2y-3/2)^2
=x^2-(4y^2-6y+9/4)
=x^2-4y^2+6y-9/4
3 (x+3)(x^2+9)(x-3)
=(x+3)(x-3)(x^2+9)
=(x^2-9)(x^2+9)
=x^4-81