Se a+b=10a + b = 10a+b=10, qual é o valor máximo de ababab?
ab=(a+b)2−(a−b)24=100−(a−b)24≤1004=25ab = \frac{(a+b)^{2} - (a-b)^{2}}{4} = \frac{100 - (a-b)^{2}}{4} \le \frac{100}{4} = 25ab=4(a+b)2−(a−b)2=4100−(a−b)2≤4100=25, since (a−b)2≥0(a-b)^{2} \ge 0(a−b)2≥0. Equality when a=b=5a = b = 5a=b=5.