Question

请验证下列等式是否成立(3^3+2^3)/(3^3+1^3)=(3+2)/(3+1) ,(4^3+3^3)/(4^3+1

Answer 1

立方和公式:

x^3+y^3=(x+y)(x^2-xy+y^2)

故:

n^3+(n-1)^3=[n+(n-1)]*[n^2-n*(n-1)+(n-1)^2]=[n+(n-1)]*(n^2-n+1)

n^3+1^3=(n+1)(n^2-n+1)

[n^3+(n-1)^3]/(n^3+1^3)=[n+(n-1)]/(n+1)

上式成立.

(5^3+4^3)/(5^3+1^3)=(5+4)/(5+1)