Question

函数y=f(x)对任意实数x,y都有f(x+y)=f(x)+f(y)+2xy,f(1)=1.求f(0) f(2) f(3

Answer 1

f(x+y)=f(x)+f(y)+2xy

f(1+0)=f(1)+f(0)

f(1)=f(1)+f(0)

所以,f(0)=0

f(2)=f(1)+f(1)+2=4

f(3)=f(2+1)=f(2)+f(1)+4=4+1+4=9

f(4)=f(2+2)=f(2)+f(2)+8=16