Thread: Simultaneous equations

Hello, I've a problem with equations. It's very hard to me. Could u give the solutions with some steps?10(b^3)=8c+2(a^5)10(c^3)=8a+2(b^5)10(a^3)=8b +2(c^5)I think, that:x,y,z=0x,y,z=1but what's next?x=? y=? z=?I need help.Thanks in advance

Originally Posted by Helloworld

Hello, I've a problem with equations. It's very hard to me. Could u give the solutions with some steps?10(b^3)=8c+2(a^5)10(c^3)=8a+2(b^5)10(a^3)=8b +2(c^5)I think, that:x,y,z=0x,y,z=1but what's next?x=? y=? z=?I need help.Thanks in advance

Let's write this out a little more intelligibly:


I suppose as a first step I'd write out:






-Dan

Originally Posted by topsquark

I presume a, b, and c are to be positive integers.

I can't finish this for you, but I will note a couple of points that you might be able to put together.

The first equation says that


1) So must be divisible by c. Similarly from the second equation must be divisible by a.

2) The RHS of both the first and second equations is divisible by 2. Thus b is divisible by 2.

3) Using 2), we see from the third equation that c is also divisible by 2.

(So note that your solution of a = 1, b = 1, and c = 1 must be incorrect.)

See if these observations get you anywhere.

-Dan

Originally Posted by Helloworld

Hello, I've a problem with equations. It's very hard to me. Could u give the solutions with some steps?10(b^3)=8c+2(a^5)10(c^3)=8a+2(b^5)10(a^3)=8b +2(c^5)I think, that:x,y,z=0x,y,z=1but what's next?x=? y=? z=?I need help.Thanks in advance

Hello,

do you mean



Where does the x, y, z come from?

Originally Posted by earboth

Hello,

do you mean



Where does the x, y, z come from?

Ahhhh...That makes more sense...

-Dan

Originally Posted by earboth

Hello,

do you mean

So again we may divide each of these by 2:

I guess this would explain your (now valid) a = 1, b = 1, c = 1 solution.

It looks to me like:

implies that a and b are either both even or both odd.

Similarly the second equation implies that b and c are either both even or both odd.

Similarly the third equation, etc.

So it looks like either all of a, b, and c are even or all of a, b, and c are odd.

-Dan

Originally Posted by topsquark

So again we may divide each of these by 2:

I guess this would explain your (now valid) a = 1, b = 1, c = 1 solution.

It looks to me like:

implies that a and b are either both even or both odd.

Similarly the second equation implies that b and c are either both even or both odd.

Similarly the third equation, etc.

So it looks like either all of a, b, and c are even or all of a, b, and c are odd.

-Dan

OK, u are right. now is ok, I should divided it by 2.And what I should do now? I know, that a=b=c, but how can I check that?

ok, now I know how can I do that Topic should be closed

Originally Posted by Helloworld

Topic should be closed

click on "Thread Tools" just above your first post and then "Mark thread as solved"