已知(a+b)²=7,(a-b)²=3.求a²+b²、ab的值
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已知(a+b)²=7,(a-b)²=3.求a²+b²、ab的值
已知(a+b)²=7,(a-b)²=3.求a²+b²、ab的值
已知(a+b)²=7,(a-b)²=3.求a²+b²、ab的值
由(a+b)²=7,得
a²+b²+2ab = 7 (1)
由(a-b)²=3.,得
a²+b² -2ab = 3 (2)
(1)+(2)得 2(a²+b²) = 10 所以 a²+b² = 5
(1)-(2)得 4ab = 4 所以 ab = 1