Let A1 and d be real numbers, the first term be A1, the sum of the first n terms of the arithmetic sequence {an} with tolerance d be Sn, satisfying s5s6 + 15 = 0, then the value range of D is______ ．

Let A1 and d be real numbers, the first term be A1, the sum of the first n terms of the arithmetic sequence {an} with tolerance d be Sn, satisfying s5s6 + 15 = 0, then the value range of D is______ ．

Because s5s6 + 15 = 0, so (5A1 + 10d) (6A1 + 15d) + 15 = 0, sorted out as 2A12 + 9a1d + 10d2 + 1 = 0, this equation can be regarded as a univariate quadratic equation about A1, it must have roots, so △ = (9D) 2-4 × 2 × (10d2 + 1) = d2-8 ≥ 0, sorted out as D2 ≥ 8, solved as D ≥ 22, or D ≤ - 22, then the value range of D is (− ∞, − & nbsp; 22] ∪ [22, + ∞); 22]∪[22，+∞)．

Let A1 and d be real numbers, the first term be A1, the sum of the first n terms of the arithmetic sequence {an} with tolerance d be Sn, satisfying s5s6 + 15 = 0, then the value range of D is______ ．

Because s5s6 + 15 = 0, so (5A1 + 10d) (6A1 + 15d) + 15 = 0, we can get 2A12 + 9a1d + 10d2 + 1 = 0. This equation can be regarded as a quadratic equation with one variable about A1, it must have roots, so △ = (9D) 2-4 × 2 × (10d2 + 1) = d2-8 ≥ 0, we can get D2 ≥ 8, we can get D ≥ 22, or D ≤ - 22, then the value range of D is (− ∞, − & nbsp; 22]; [22, + ∞). So the answer is: (− ∞, − & nbsp; 22]; [22, + ∞)