Let a, B, C be the three sides of the triangle ABC, and satisfy (1) a > b > C; (2) 2B = a + C; (3) A2 + B2 + C2 = 84, then the integer B=______ ．

Let a, B, C be the three sides of the triangle ABC, and satisfy (1) a > b > C; (2) 2B = a + C; (3) A2 + B2 + C2 = 84, then the integer B=______ ．

∵ a, B, C are three sides of the triangle ABC, and satisfy a ＞ B ＞ C, 2b = a + C, ∵ a ＞ C ＞ 0, ∵ a, C are two unequal positive roots of the quadratic equation x2 − 2bx + 5b2 − 842 = 0 about X, ∵ Δ= 4B2 − 2 (5b2 − 84) ＞ 02B ＞ 05b2 − 842 ＞ 0 ∵ the result of the solution is 844 ＜ B2 ＜ 28 ∵ B is an integer, B ＞ 0, ∵ B2 = 25, ∵ B = 5

Let a, B, C be the three sides of the triangle ABC, and satisfy (1) a > b > C; (2) 2B = a + C; (3) A2 + B2 + C2 = 84, then the integer B=______ ．

∵ a, B, C are three sides of the triangle ABC, and satisfy a ＞ B ＞ C, 2b = a + C, ∵ a ＞ C ＞ 0, ∵ a, C are two unequal positive roots of the quadratic equation x2 − 2bx + 5b2 − 842 = 0 about X, ∵ Δ= 4B2 − 2 (5b2 − 84) ＞ 02B ＞ 05b2 − 842 ＞ 0 ∵ the result of the solution is 844 ＜ B2 ＜ 28 ∵ B is an integer, B ＞ 0, ∵ B2 = 25, ∵ B = 5

It is known that the trilateral lengths of △ ABC are a, B, C, and satisfy: (1) a > b > C, (2) 2B = a + C, (3) B is a positive integer, (4) a & # 178; + B & # 178; + C & # 178; = 84,
Finding the value of B