由 宇智波鼬 於 星期日 三月 18, 2007 5:48 pm
Let me put it this way...
a+(1/a)>=2>1. So, when a or 1/a increases, a+(1/a) will also increase.
That means the min value of a+(1/a) appears when a=1/a.
The situation b is the same.
a^3+b^3+3ab=1 tells us a is not equal to 1.
But obviously, we'll get the min when a=b.
Solve the equation: 2a^3+3a^2=1.
We get a=-1 or 1/2.
a is postive real, so we choose 1/2.
That's how we get the answer.