determining the smallest value.

[mark10245]

Hey,

Can you please solve this for me?

The task is:

Determine the smallest possible value of the expression a+b³, where a and b are positive and their product is equal to 1.

 

[Ishuda]

Hey,

Can you please solve this for me?

The task is:

Determine the smallest possible value of the expression a+b³, where a and b are positive and their product is equal to 1.

Since this is the Algebra forum, I suppose we can't use calculus to find out that the answer is a = 3^1/4 and b = 3^-1/4. So we need to find the minimum of
\(\displaystyle f(b) = \frac{1}{b} + b^3\) or \(\displaystyle f(a) = a + \frac{1}{a^3}\)
without using anything beyond algebra. Haven't found a nice solution yet.

 

[lookagain]

Hey,

Can you please solve this for me?

The task is:

Determine the smallest possible value of the expression a+b³, where a and b are positive and their product is equal to 1.

mark10245,

tell us the level of mathematics course you are in that you were given this problem.