已知a,b,c都是整数,且3分之a=4分之b=2分之c,ab+bc+ac=52,求a,b,c的值

设 3分之a = 4分之b = 2分之c = k 则 a = 3k , b = 4k , c = 2k ab + bc + ac = 52 12k² + 8k² + 6k² = 52 26k² = 52 k² = 2 k = √2 或 k = -√2 因为 a,b,c都是正数 所以 k > 0 所以 k = √2 所以 a = 3k = 3√2 b = 4k = 4√2 c = 2k = 2√2