已知m²-mn=21,mn-n²=-15,求代数式m²-n²与m²-2mn+n²的值
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![已知m²-mn=21,mn-n²=-15,求代数式m²-n²与m²-2mn+n²的值](/uploads/image/z/184181-5-1.jpg?t=%E5%B7%B2%E7%9F%A5m%26%23178%3B-mn%3D21%2Cmn-n%26%23178%3B%3D-15%2C%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8Fm%26%23178%3B-n%26%23178%3B%E4%B8%8Em%26%23178%3B-2mn%2Bn%26%23178%3B%E7%9A%84%E5%80%BC)
已知m²-mn=21,mn-n²=-15,求代数式m²-n²与m²-2mn+n²的值
已知m²-mn=21,mn-n²=-15,求代数式m²-n²与m²-2mn+n²的值
已知m²-mn=21,mn-n²=-15,求代数式m²-n²与m²-2mn+n²的值
m²-mn=21
mn-n²=-15
两式相加的m²-n²=6
两式相减m²-mn-(mn-n²)=21-(-15)=36
即m²-2mn+n²=36
m²-n²=(m²-mn)+(mn-n²)=21-15=6
m²-2mn+n²=(m²-mn)-(mn-n²)=21-(-15)=36
∵m²-mn=21,mn-n²=-15
∴m²-n²=(m²-mn)+(mn-n²)=6
m²-2mn+n² =(m²-mn)-(mn-n²)=36
两式相加得m^2-n^2=6,
两式相减得m^2-2mn+n^2=36