\u30b5\u30a4\u30b3\u30ed\u3092 \\(3\\) \u56de\u6295\u3052\u3066\u51fa\u305f\u76ee\u3092\u9806\u306b \\(a , b , c\\) \u3068\u3059\u308b\u3068\u304d,\r\n\\[\r\n\\displaystyle\\int _ {a-3}^{a+3} (x-b) (x-c) \\, dx = 0\r\n\\]\r\n\u3068\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p>\r\n
\u30b5\u30a4\u30b3\u30ed\u306e\u76ee\u306e\u51fa\u65b9\u306f \\(6^3\\) \u901a\u308a.\r\n\\[\\begin{align}\r\n\\displaystyle\\int _ {a-3}^{a+3} (x-b) (x-c) \\, dx & = \\left[ \\dfrac{x^3}{3} -(b+c) \\dfrac{x^2}{2} +bc x \\right] _ {a-3}^{a+3} \\\\\r\n& = \\dfrac{1}{3} (a+3)^3 -\\dfrac{1}{2} (b+c) (a+3)^2 +bc (a+3) \\\\\r\n& \\qquad -\\dfrac{1}{3} (a-3)^3 +\\dfrac{1}{2} (b+c) (a-3)^2 -bc (a+3) \\\\\r\n& = 6 ( a^2 +3 ) -6 (b+c) a +6bc = 0\r\n\\end{align}\\]\r\n\u3086\u3048\u306b\r\n\\[\\begin{align}\r\na^2 -a (b+c) +bc & = -3 \\\\\r\n(a-b) (a-c) & = -3 \\\\\r\n\\text{\u2234} \\quad ( a-b \\, , \\, a-c ) & = ( \\pm 1 , \\mp 3 ) , ( \\pm 3 , \\mp 1 ) \\quad ( \\text{\u8907\u53f7\u540c\u9806} )\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\na = b \\pm 1 = c \\mp 3 \\ \\text{\u307e\u305f\u306f} \\ a = b \\pm 3 = c \\mp 1 \\quad ( \\text{\u8907\u53f7\u540c\u9806} )\r\n\\]\r\n\u3053\u308c\u3092\u3068\u304f\u3068\r\n\\[\\begin{align}\r\n( a , b , c ) = & ( 2 , 1 , 5 ) , ( 3 , 2 , 6 ) , ( 4 , 5 , 1 ) , ( 5 , 6 , 2 ) , \\\\\r\n& ( 4 , 1 , 5 ) , ( 5 , 2 , 6 ) , ( 2 , 5 , 1 ) , ( 3 , 6 , 2 )\r\n\\end{align}\\]\r\n\u3067, \u6761\u4ef6\u3092\u307f\u305f\u3059\u7d44\u306f \\(8\\) \u7d44.
\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{8}{6^3} = \\underline{\\dfrac{1}{27}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u30b5\u30a4\u30b3\u30ed\u3092 \\(3\\) \u56de\u6295\u3052\u3066\u51fa\u305f\u76ee\u3092\u9806\u306b \\(a , b , c\\) \u3068\u3059\u308b\u3068\u304d, \\[ \\displaystyle\\int _ {a-3}^{a+3} (x-b) (x-c) \\, dx = 0 \\] \u3068\u306a\u308b\u78ba\u7387\u3092 … \u7d9a\u304d\u3092\u8aad\u3080