It is known that the opposite sides of the three inner angles a, B and C of △ ABC are a, B and C respectively. If a, B and C form an arithmetic sequence and 2cos2b-8cosb + 5 = 0, the size of angle B is calculated and the shape of △ ABC is judged

It is known that the opposite sides of the three inner angles a, B and C of △ ABC are a, B and C respectively. If a, B and C form an arithmetic sequence and 2cos2b-8cosb + 5 = 0, the size of angle B is calculated and the shape of △ ABC is judged


From 2cos2b-8cosb + 5 = 0, we can get 4cos2b-8cosb + 3 = 0, that is, (2cosb-1) (2cosb-3) = 0. The solution is CoSb = 12 or CoSb = 32 (rounding off). ∵ 0 < B < π, ∵ B = π 3 and ∵ a, B, C form an arithmetic sequence, that is, a + C = 2B. ∵ CoSb = A2 + C2 − b22ac = A2 + C2 − (a + C2) 22ac = 12. The simplification is A2 + c2-2ac = 0, the solution is a = C, ∵ B = π 3 ∵ ABC is an equilateral triangle



It is known that the opposite sides of the three inner angles a, B and C of △ ABC are a, B and C respectively. If a, B and C form an arithmetic sequence and 2cos2b-8cosb + 5 = 0, the size of angle B is calculated and the shape of △ ABC is judged


From 2cos2b-8cosb + 5 = 0, we can get 4cos2b-8cosb + 3 = 0, that is, (2cosb-1) (2cosb-3) = 0. The solution is CoSb = 12 or CoSb = 32 (rounding off). ∵ 0 < B < π, ∵ B = π 3 and ∵ a, B, C form an arithmetic sequence, that is, a + C = 2B. ∵ CoSb = A2 + C2 − b22ac = A2 + C2 − (a + C2) 22ac = 12. The simplification is A2 + c2-2ac = 0, the solution is a = C, ∵ B = π 3 ∵ ABC is an equilateral triangle



It is known that the opposite sides of the three inner angles a, B and C of △ ABC are a, B and C respectively. If a, B and C form an arithmetic sequence and 2cos2b-8cosb + 5 = 0, the size of angle B is calculated and the shape of △ ABC is judged


From 2cos2b-8cosb + 5 = 0, we can get 4cos2b-8cosb + 3 = 0, that is, (2cosb-1) (2cosb-3) = 0. The solution is CoSb = 12 or CoSb = 32 (rounding off). ∵ 0 < B < π, ∵ B = π 3 and ∵ a, B, C form an arithmetic sequence, that is, a + C = 2B. ∵ CoSb = A2 + C2 − b22ac = A2 + C2 − (a + C2) 22ac = 12. The simplification is A2 + c2-2ac = 0, the solution is a = C, ∵ B = π 3 ∵ ABC is an equilateral triangle



It is known that the opposite sides of the three inner angles a, B and C of △ ABC are a, B and C respectively. If a, B and C form an arithmetic sequence and 2cos2b-8cosb + 5 = 0, the size of angle B is calculated and the shape of △ ABC is judged


From 2cos2b-8cosb + 5 = 0, we can get 4cos2b-8cosb + 3 = 0, that is, (2cosb-1) (2cosb-3) = 0. The solution is CoSb = 12 or CoSb = 32 (rounding off). ∵ 0 < B < π, ∵ B = π 3 and ∵ a, B, C form an arithmetic sequence, that is, a + C = 2B. ∵ CoSb = A2 + C2 − b22ac = A2 + C2 − (a + C2) 22ac = 12. The simplification is A2 + c2-2ac = 0, the solution is a = C, ∵ B = π 3 ∵ ABC is an equilateral triangle