Question

关于整式公式的问题a+b=p,ab=q,则a^5+b^5=?

Answer 1

a^5+b^5=(a^3+b^3)(a^2+b^2)-(ab)^2*(a+b) (1)

a^2+b^2=(a+b)^2-2ab=p^2-2q (2)

a^3+b^3=(a+b)^3-3ab(a+b)=p^3-3pq (3)

把(2)和(3)代入(1)

得:a^5+b^5=p^5-5qp^3+5pq^2