Question

解方程： 4x²-（x+1）²=0

解方程：
4x²-（x+1）²=0
计算：
计算：
1-2²+3²-4²+5²-6²+·····+99²-100²

Answer 1

4x²-(x-1)²=0
(2x+x-1)(2x-x+1)=0
(3x-1)(x+1)=0
x1=1/3 x2=-1
(1-1/2²)(1-1/3²)……(1-1/100²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/100)(1+1/100)
=[(1-1/2)(1-1/3)……(1-1/100)]×[(1+1/2)(1+1/3)……(1+1/100)]
=(1/100)×(101/2)
=101/200
1²-2²+3²-4²+……+99²-100²
=(1-2)(1+2)+(3-4)(3+4)+……+(99-100)(99+100)
=-1-2-3-4-……-99-100
=-5050