CalculatorUser

Let us ponder about that.

Wow.... you are TALL

I am 5'7'' too!
 

Except I am in 8th grade lol

Never mind, you said "sis" 

That must mean that Magic Kitten is your sister!

How do you know? 

Wow, you are 6 feet already, you sure are healthy!

What the question means is that:

when the student substituted a number for \(x\) in \((2x)^3\), the result was \(384\) larger than substituting for \(2x^3\).

So find X.

\(2x^3+384=(2x)^3\)

\(2x^3+384=8x^3\)

\(6x^3=384\)

\(x^3=64\)

\(x=4\)

The answer should be 4.

yeah, don't inhale accelerator.

and wash your hands after using superglue.

I learned the lesson by having a sudden bout of nausea and almost threw up.

\(\frac{3}{x} + \frac{2}{y}\)

Simplifies to

\(\frac{2x+3y}{xy}\)

Then we substitute in \(2x + 3y = 5\)

SO we have, \(\frac{5}{xy}\)

Since x and y MUST be positive real numbers, the product of XY must be as large as possible.

This means:

1) X and Y must be as close to possible

2) X and Y must satisfy 2x + 3y = 5.

3) they are positive

This is easy, the values of X and Y respectively must be (1, 1). They are as close as possible, AND they satisfy the equation

So the minimum value is

\(\frac{5}{1}\)

which is equal to (drumroll please)

\(\boxed{5}\)

A solution by Art of Problem Solving