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