关于初二数学题1.(x+y)^3-(x-y)^2(x+y)2.已知a+b=1,求证a^3+b^3+3ab=1
问题描述:
关于初二数学题
1.(x+y)^3-(x-y)^2(x+y)
2.已知a+b=1,求证a^3+b^3+3ab=1
答
(1)(X+Y)³-(X-Y)²(X+Y)
=(X+Y)〔(X+Y)²-(X-Y)²〕
=(X+Y)(X+Y+X-Y)(X+Y-X+Y)
=4XY(X+Y)
(2)(a+b)³
=a³+b³+3a²b+3ab²
=a³+b³+3ab(a+b)
因为a+b=1,所以(a+b)³=a³+b³+3ab
a+b=1,因此(a+b)³=1
所以a³+b³+3ab=1