已知(m+n)²=7,(m-n)²=3,(m-n)²=3,求下列各式的值:(1)mn;(2)m²+n²
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![已知(m+n)²=7,(m-n)²=3,(m-n)²=3,求下列各式的值:(1)mn;(2)m²+n²](/uploads/image/z/1124128-64-8.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%88m%2Bn%29%26%23178%3B%3D7%2C%EF%BC%88m-n%EF%BC%89%26%23178%3B%3D3%2C%EF%BC%88m-n%EF%BC%89%26%23178%3B%3D3%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC%EF%BC%9A%EF%BC%881%EF%BC%89mn%EF%BC%9B%EF%BC%882%EF%BC%89m%26%23178%3B%2Bn%26%23178%3B)
已知(m+n)²=7,(m-n)²=3,(m-n)²=3,求下列各式的值:(1)mn;(2)m²+n²
已知(m+n)²=7,(m-n)²=3,(m-n)²=3,求下列各式的值:(1)mn;(2)m²+n²
已知(m+n)²=7,(m-n)²=3,(m-n)²=3,求下列各式的值:(1)mn;(2)m²+n²
(m+n)²=m²+2mn+n²=7
(m-n)²=m²-2mn+n²=3
上面两式相减得4mn=4 mn=1
上面两式相加得2m²+2n²=10 m²+n²=5
不懂的再追问
(m+n)² = 7 (1)
(m-n)² = 3 (2)
(1)-(2) 得
4mn = 4
mn = 1
m²+n² = 7 -2mn = 5