现定义某种运算“★”,对于任意两个数a,b,都有a★b=a的平方-ab+b的平方.例如:3★4=3的平方-3×4+4的平方=9-12+16=13(a+1)★(a+2)=(a+b)★(a-b)
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![现定义某种运算“★”,对于任意两个数a,b,都有a★b=a的平方-ab+b的平方.例如:3★4=3的平方-3×4+4的平方=9-12+16=13(a+1)★(a+2)=(a+b)★(a-b)](/uploads/image/z/1016702-62-2.jpg?t=%E7%8E%B0%E5%AE%9A%E4%B9%89%E6%9F%90%E7%A7%8D%E8%BF%90%E7%AE%97%E2%80%9C%E2%98%85%E2%80%9D%2C%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E4%B8%A4%E4%B8%AA%E6%95%B0a%2Cb%2C%E9%83%BD%E6%9C%89a%E2%98%85b%3Da%E7%9A%84%E5%B9%B3%E6%96%B9%EF%BC%8Dab%2Bb%E7%9A%84%E5%B9%B3%E6%96%B9.%E4%BE%8B%E5%A6%82%EF%BC%9A%EF%BC%93%E2%98%85%EF%BC%94%3D%EF%BC%93%E7%9A%84%E5%B9%B3%E6%96%B9-%EF%BC%93%C3%97%EF%BC%94%2B%EF%BC%94%E7%9A%84%E5%B9%B3%E6%96%B9%3D%EF%BC%99-%EF%BC%91%EF%BC%92%2B%EF%BC%91%EF%BC%96%3D%EF%BC%91%EF%BC%93%28a%2B1%29%E2%98%85%28a%2B2%29%3D%28a%2Bb%29%E2%98%85%28a-b%29)
现定义某种运算“★”,对于任意两个数a,b,都有a★b=a的平方-ab+b的平方.例如:3★4=3的平方-3×4+4的平方=9-12+16=13(a+1)★(a+2)=(a+b)★(a-b)
现定义某种运算“★”,对于任意两个数a,b,都有a★b=a的平方-ab+b的平方.例如:3★4=3的平方-3×4+4的平方=9-12+16=13
(a+1)★(a+2)=
(a+b)★(a-b)
现定义某种运算“★”,对于任意两个数a,b,都有a★b=a的平方-ab+b的平方.例如:3★4=3的平方-3×4+4的平方=9-12+16=13(a+1)★(a+2)=(a+b)★(a-b)
原式=a²+2a+1-(a²+3a+2)+a²+4a+4=a²+3a+3.
原式=(a+b)²-(a²-b²)+(a-b)²=a²-2ab+3b.
(a+1)★(a+2)
=(a+1)²-(a+1)(a+2)+(a+2)²
=a²+2a+1-(a²+3a+2)+(a²+4a+4)
=a²+2a+1-a²-3a-2+a²+4a+4
=a²+3a+3
(a+b)★(a-b)
=(a+b)...
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(a+1)★(a+2)
=(a+1)²-(a+1)(a+2)+(a+2)²
=a²+2a+1-(a²+3a+2)+(a²+4a+4)
=a²+2a+1-a²-3a-2+a²+4a+4
=a²+3a+3
(a+b)★(a-b)
=(a+b)²-(a+b)(a-b)+(a-b)²
=a²+2ab+b²-(a²-b²)+(a²-2ab+b²)
=a²+2ab+b²-a²+b²+a²-2ab+b²
=a²+3b²
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后面是求证麽