math problems

• May 12th 2006, 12:10 AM
sophea
Hello! I have a problem.
Hello I have a problem.
We have X+Y+Z+W=X²+Y²+Z²+W²=0
What the value of x,y,z,w?
• May 12th 2006, 12:41 AM
CaptainBlack
Quote:

Originally Posted by sophea
Hello I have a problem.
We have X+Y+Z+W=X²+Y²+Z²+W²=0
What the value of x,y,z,w?

Since $X^2,\ Y^2,\ Z^2, W^2 \ge 0$ if their sum is $0$ they must individualy all be [math0[/tex], so:

$
X=Y=Z=W=0
$

RonL

end of an old unrelated thread
• May 21st 2006, 06:26 PM
sophea
Quote:

Originally Posted by CaptainBlack
Since $X^2,\ Y^2,\ Z^2, W^2 \ge 0$ if their sum is $0$ they must individualy all be [math0[/tex], so:

$
X=Y=Z=W=0
$

RonL

end of an old unrelated thread

Ok! thank you very for you solution.
now i have one more problem:
X².X²=2X² +[X]
Note: X-1<[X] <X
• May 21st 2006, 09:55 PM
CaptainBlack
Quote:

Originally Posted by sophea
Ok! thank you very for you solution.
now i have one more problem:
X².X²=2X² +[X]
Note: X-1<[X] <X

There is a limited range of $X$ over which this can have a solution. For
instance the inequality cannot hold if $|X| \ge 2.5$ . So plug in $-2,-1,0,1,2$ in
turn for $[X]$ and then solve for $X$ . Keep any solutions for which $[X]$ is
equal to the assumed value used.

As an example we will work the case where we assume $[X]=-2$ .

Then we want solutions of:

$
X^4=2 X^2-2
$

which is a quadratic in $X^2$ , so using the quadratic formula:

$
X^2=1 \pm \sqrt{-1}
$
,

which is complex and so not an admissible solution (I will assume we want
real solutions).

Now lets try assuming $[X]=-1$ , then:

$
X^2=1 \pm \sqrt{0}=1,
$

and so $X=\pm 1$ are solutions of this equation and $X=-1$ is consistent with
our assumption and so is a solution of the original problem.

Carrying on like this you will find all of the remaining solutions.

RonL
• May 22nd 2006, 07:48 PM
mpgc_ac
Quote:

Originally Posted by CaptainBlack
There is a limited range of $X$ over which this can have a solution. For
instance the inequality cannot hold if $|X| \ge 2.5$ . So plug in $-2,-1,0,1,2$ in
turn for $[X]$ and then solve for $X$ . Keep any solutions for which $[X]$ is
equal to the assumed value used.

As an example we will work the case where we assume $[X]=-2$ .

Then we want solutions of:

$
X^4=2 X^2-2
$

which is a quadratic in $X^2$ , so using the quadratic formula:

$
X^2=1 \pm \sqrt{-1}
$
,

which is complex and so not an admissible solution (I will assume we want
real solutions).

Now lets try assuming $[X]=-1$ , then:

$
X^2=1 \pm \sqrt{0}=1,
$

and so $X=\pm 1$ are solutions of this equation and $X=-1$ is consistent with
our assumption and so is a solution of the original problem.

Carrying on like this you will find all of the remaining solutions.

RonL

Dear sir!
How smart you are!
I'm realy happy to saw your solution.
Now i have one more problem and I hope you are not feel borred because I always have more and more problem.
My problem is:
In ABC rectangle have BO bisects CBA , CO bisects ACB, MN // BC .
FInd the perimeter of AMN rectangle. Thank you advance.