Math wizards
#29
Re: Math wizards
i know this really doesn't help now that you had to turn it in, but using your definition of the arithmetic-geometric mean inequality and the theorem you can see:
1. the inequality is ≤, so the maximum of the cube root (which would be the maximum of the products also) is when the both sides of the inequality are equal. Your definition says that the equality holds only if a=b=c.
2. using this information, one can see that stu (or abc) would be the a maximun (have the highest cube root) when s=t=u (or a=b=c)
I hope this makes sense, and again I am sorry I didn't see until now.
1. the inequality is ≤, so the maximum of the cube root (which would be the maximum of the products also) is when the both sides of the inequality are equal. Your definition says that the equality holds only if a=b=c.
2. using this information, one can see that stu (or abc) would be the a maximun (have the highest cube root) when s=t=u (or a=b=c)
I hope this makes sense, and again I am sorry I didn't see until now.