Minimum value

For discussing Olympiad Level Algebra (and Inequality) problems
lizzythebest
Posts: 3
Joined: Mon Jul 03, 2017 4:05 pm

Minimum value

Unread post by lizzythebest » Sat Jul 22, 2017 3:18 pm

Determine the minimum value of
$\frac{4x^3}{y}+\frac{y+1}{x}$

with $x>0$ and $y>0$ real numbers.

Ragib Farhat Hasan
Posts: 44
Joined: Sun Mar 30, 2014 10:40 pm

Re: Minimum value

Unread post by Ragib Farhat Hasan » Thu Sep 27, 2018 7:31 pm

Apparently, the denominators should be 1. So the minimum value will be 6.

NABILA
Posts: 28
Joined: Sat Dec 15, 2018 5:19 pm
Location: Munshigonj, Dhaka

Re: Minimum value

Unread post by NABILA » Sat Dec 15, 2018 7:39 pm

No.
If, X>0, y>0
Then, it could be x=y=0.1 or 0.01 or 0.000001
Because, x and y are real number.

NABILA
Posts: 28
Joined: Sat Dec 15, 2018 5:19 pm
Location: Munshigonj, Dhaka

Re: Minimum value

Unread post by NABILA » Mon Dec 17, 2018 6:11 pm

Ragib Farhat Hasan wrote:
Thu Sep 27, 2018 7:31 pm
Apparently, the denominators should be 1. So the minimum value will be 6.
I don't think so. Bcoz, x>0 and y>0 are real numbers not natural.

Ragib Farhat Hasan
Posts: 44
Joined: Sun Mar 30, 2014 10:40 pm

Re: Minimum value

Unread post by Ragib Farhat Hasan » Sun Sep 15, 2019 1:49 am

NABILA wrote:
Mon Dec 17, 2018 6:11 pm
Ragib Farhat Hasan wrote:
Thu Sep 27, 2018 7:31 pm
Apparently, the denominators should be 1. So the minimum value will be 6.
I don't think so. Bcoz, x>0 and y>0 are real numbers not natural.
I know the difference.

What I meant was: in the solution to the problem, both $x$ and $y$ should be 1.

BTW, this is just an observation since I didn't go through with the solution; it is an "apparent result".

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