设a.b为实数,求a²+2ab-2b²-4b+5的最小值,并求此时a与b的值.急用阿
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![设a.b为实数,求a²+2ab-2b²-4b+5的最小值,并求此时a与b的值.急用阿](/uploads/image/z/754054-70-4.jpg?t=%E8%AE%BEa.b%E4%B8%BA%E5%AE%9E%E6%95%B0%2C%E6%B1%82a%26%23178%3B%2B2ab-2b%26%23178%3B-4b%2B5%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%2C%E5%B9%B6%E6%B1%82%E6%AD%A4%E6%97%B6a%E4%B8%8Eb%E7%9A%84%E5%80%BC.%E6%80%A5%E7%94%A8%E9%98%BF)
设a.b为实数,求a²+2ab-2b²-4b+5的最小值,并求此时a与b的值.急用阿
设a.b为实数,求a²+2ab-2b²-4b+5的最小值,并求此时a与b的值.急用阿
设a.b为实数,求a²+2ab-2b²-4b+5的最小值,并求此时a与b的值.急用阿
a²+2ab+2b²-4b+5
=(a+b)²+b²-4b+5
=(a+b)²+(b-2)²+1
所以
当a+b=0,b-2=0时
即
a=-2
b=2
时
有最小值=1
a²+2ab+2b²-4b+5
=a²+2ab+b²+b²-4b+5
=(a+b)²+(b-2)²+1
因:(a+b)² ≥0, (b-2)²≥0
所以当:(a+b)²=(b-2)²=0时有最小值1,此时有:
b=2,a=-2