Question

a,b为任意实数,3a+4b=1,则a＾2+b＾2的最小值是多少?

Answer 1

3a+4b=1

得,a=(1-4b)/3,代入

a²+b²

=[(1-4b)/3]²+b²

=(1-8b+16b²)/9+b²

=(25b²/9-8b/9)+1/9

=[(5b/3)-(4/15)]²+1/9-(4/15)²

>=1/9-16/225

=9/225

=1/25