# Solving simultaneous equation and inequation subject to constraints.

• Apr 10th 2010, 12:13 AM
smallchicken1205
Solving simultaneous equation and inequation subject to constraints.
Let a, b, c be positive real number satisfying:
$\displaystyle \frac{1}{a+b+1}+\frac{1}{b+c+1} +\frac{1}{c+a+1}\geq1$
Prove that $\displaystyle a+b+c=ab+bc+ca$

Find all real numbers k and m and satisfying:
$\displaystyle k(x^3+y^3+z^3)+mxyz\geq(x+y+z)^3$
with all $\displaystyle x,y,z$non-negative.

Solve this equations:
$\displaystyle \sqrt[2]{y^2-8x+9}-\sqrt[3]{xy-6x+12}\leq1$and $\displaystyle \sqrt{2(x-y)^2+10x-6y+12}-\sqrt{y}=\sqrt{x+2}$

Thank you very much!
• Apr 10th 2010, 04:54 AM
mathemagister
Quote:

Originally Posted by smallchicken1205
Let a, b, c be positive real number satisfying:
$\displaystyle \frac{1}{a+b+1}+\frac{1}{b+c+1} +\frac{1}{c+a+1}\geq1$
Prove that $\displaystyle a+b+c=ab+bc+ca$

Find all real numbers k and m and satisfying:
$\displaystyle k(x^3+y^3+z^3)+mxyz\geq(x+y+z)^3$
with all $\displaystyle x,y,z$non-negative.

Solve this equations:
$\displaystyle \sqrt[2]{y^2-8x+9}-\sqrt[3]{xy-6x+12}\leq1$and $\displaystyle \sqrt{2(x-y)^2+10x-6y+12}-\sqrt{y}=\sqrt{x+2}$

Thank you very much!

This looks a lot like homework. Please show us what you have done so far to show that you have at least attempted something. Then ask here about the parts you are stuck on. That way, you are following MHF Policy.
Also, don't ask more than 2 questions in the same thread, which potentially makes the thread difficult to follow.

Thanks
Mathemagister

PS Sorry if I sound too admin-like.
• Apr 10th 2010, 05:30 AM
smallchicken1205
I think in 1st problem, maybe it must be $\displaystyle a+b+c\geq ab+bc+ca$