已知:三個連續(xù)奇數(shù),它們的平方和為251,求這三個奇數(shù)分別為________.
7,9,11或-11,-9,-7
分析:設(shè)這三個奇數(shù)為2n-1,2n+1,2n+3根據(jù)題意列方程求解.
解答:設(shè)這三個奇數(shù)為2n-1,2n+1,2n+3
(2n-1)2+(2n+1)2+(2n+3)2=251
n=4或n=-5
當n=4時,奇數(shù)為7,9,11
當n=-5時,奇數(shù)為-11,-9,-7
故答案為7,9,11或-11,-9,-7
點評:本題的關(guān)鍵是能準確設(shè)出奇數(shù)為2n-1,2n+1,2n+3,然后根據(jù)題意列方程求解即可.