Matematické Fórum

stuart clark · 08. 07. 2012 08:14

If $x,y,z\in\mathbb{R}$ and $x+y+z=0$ and $\mid x \mid+\mid y \mid+\mid z \mid\neq 0$ . Then Max. and Min. value of $\frac{\sqrt{x^2+y^2+z^2}}{\mid x \mid+\mid y \mid+\mid z \mid}$

vanok · 14. 07. 2012 12:18

Hi ↑ stuart clark:,
Thanks to homogeneity of the problem, it is enough to solve this problem:
If $X,Y\in\mathbb{R}$ and $X+Y+1=0$ and $\mid X \mid+\mid Y \mid+1\neq 0$ . Then Max. and Min. value of $\frac{\sqrt{X^2+Y^2+1}}{\mid X \mid+\mid Y \mid+1}$

To solve it let us envisage 3 cases:
a) $X \leq 0; Y \leq 0$
b) $X \leq 0; Y \geq 0$
and similarly
c) $X \geq 0; Y \leq 0$

Now to end the problem is very simple.

Matematické Fórum

#1 08. 07. 2012 08:14

Max.,Min. Complex no.

#2 14. 07. 2012 12:18

Re: Max.,Min. Complex no.

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