若(2x+1)11=a0+a1x+a2x2+…+a11x11，则(a0+a2+…+a10)2-(a1+a3+…+a11)2=．

Question

若 (2x+1 ) 11 = a 0 + a 1 x+ a 2 x 2 +…+ a 11 x 11 ，则 ( a 0 + a 2 +…+ a 10 ) 2 -( a 1 + a 3 +…+ a 11 ) 2 =______．

Answer 1

∵ (2x+1 ) 11 = a 0 + a 1 x+ a 2 x 2 +…+ a 11 x 11 ，令x=1可得a ₀ +a ₁ +a ₂ +a ₃ +…+a ₁₁ =3 ¹¹ ．
再令x=-1可得（a ₀ +a ₂ +a ₄ +…+a ₁₀ ）-（a ₁ +a ₃ +a ₅ +…+a ₁₁ ）=-1．
两式相乘可得 ( a 0 + a 2 +…+ a 10 ) 2 -( a 1 + a 3 +…+ a 11 ) 2 =-3 ¹¹ ，
故答案为-3 ¹¹ ．