Question

已知实数a.b,满足1/2的a次方+1/2的b次方=1,1/2的a+b次方+1/2的a+c次方+1/2的b+c次方=1,

Answer 1

0.5^a+0.5^b=1,0.5^(a+b)+0.5^(a+c)+0.5^(b+c)=1

所以0.5^c=1+0.5^(2b)-0.5^b

当c取最大值时,0.5^c取最小值,因为0.5^c是关于c的减函数,

令0.5^b=t>0

则0.5^c=t^2-t+1=(t-0.5)^2+0.75

所以当t=0.5时,即b=1,时

0.5^c有最小值0.75

此时C=ln0.75/ln0.5=0.415037