Question

已知a,b,c为等差数列,且a+b+c=12,abc=48求a,b,c的值

Answer 1

问：已知a,b,c为等差数列,且a+b+c=12,abc=48求a,b,c的值

答：同学你好，设等差数列公差为d，则有：b = a + d，c = a + 2d代入a+b+c=12得：a + (a+d) + (a+2d) = 12化简得：3a + 3d = 12即：a + d = 4代入abc=48得：a(a+d)(a+2d) = 48代入a+d=4得：a(4)(a+2d) = 48化简得：a^2 + 2ad - 12 = 0代入求根公式得：a = 2或a = -6若a = 2，则d = 2，b = 4，c = 6若a = -6，则d = 5，b = -4，c = 13由于等差数列的定义，b和c不能为负数，因此舍去a=-6，最终得到答案：a = 2，b = 4，c = 6