Maximize This

Algebra Level 4

Positive reals x x , y y and z z are such that x + y + z = x y z x+y+z=xyz . Find the maximum value of ( x − 1 ) ( y − 1 ) ( z − 1 ) \large (x-1)(y-1)(z-1) Given the answer in 4 decimal places .


The answer is 0.3923.

Watsapol Kerdlarppol by Watsapol Kerdlarppol , 22, Thailand

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Sanjoy Kundu
Jul 31, 2017

Trivially, let x = y = z, then x^3 = 3x, solving we get x = 0, and x = +/- rad 3. The maximum occurs at x = rad 3.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Who told you to take x = y = z x=y=z directly?

Vilakshan Gupta - 2 years, 8 months ago

Log in to reply

Generally, letting x = y = z is a good guess for maximizing/minimizing a function.

Sanjoy Kundu - 2 years, 8 months ago

Log in to reply

But then why you are writing it as a solution, it's just a guess...

Vilakshan Gupta - 2 years, 8 months ago

Log in to reply

@Vilakshan Gupta – Because it's my solution...

Sanjoy Kundu - 2 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...