设实数a,b满足:3a²-10ab+8b²+5a-10b=0,求u=9a²+72b+2的最小值.
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![设实数a,b满足:3a²-10ab+8b²+5a-10b=0,求u=9a²+72b+2的最小值.](/uploads/image/z/3791071-55-1.jpg?t=%E8%AE%BE%E5%AE%9E%E6%95%B0a%2Cb%E6%BB%A1%E8%B6%B3%EF%BC%9A3a%26%23178%3B-10ab%2B8b%26%23178%3B%2B5a-10b%3D0%2C%E6%B1%82u%3D9a%26%23178%3B%2B72b%2B2%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC.)
设实数a,b满足:3a²-10ab+8b²+5a-10b=0,求u=9a²+72b+2的最小值.
设实数a,b满足:3a²-10ab+8b²+5a-10b=0,求u=9a²+72b+2的最小值.
设实数a,b满足:3a²-10ab+8b²+5a-10b=0,求u=9a²+72b+2的最小值.
(3a-4b)(a-2b)+5(a-2b)=0
(a-2b)(3a-4b+5)=0
∴a=2b或3a-4b+5=0
当a=2b时
U=9a²+36a+2=9(a²+4a+4)-34=9(a+2)²-34
当a=-2时有最小值-34,此时b=-1
当3a-4b+5=0时
4b=3a+5
u=9a²+54a+90+2=9a²+54a+81+11=9(a+3)²+11
a=-3时有最小值11
综合上面的两种情况得
a=-2,b=-1时,有最小值-34