Question

If xy = 5, xz = 10 , yz = 2, and x ,y ,z are positive, what is the value of xyz

Answer 1

@Ahaanomegas

Answer 2

I know there's a trick to this, but what's the trick?

Answer 3

\[ xy = 5 \]\[xz = 10 \]\[yz = 2 \]Multiply all three equations - the left-hand-sides and the right-hand-sides. You get: \[ x^2 y^2 z^2 = 100. \]Notice the the LHS is just \[ (xyz)^2, \]which is equal to 100. Therefore, xyz is either -10 or 10. Since x, y, and z are all positive, \[xyz=\fbox{10}.\]Hope that helped! :)

Answer 4

Helped very much!

Answer 5

No problem. Thanks for the medal and nice new avatar! :)

Answer 6

I always overlook this stuff

Answer 7

No problem. It happens! :)

Answer 8

Hahaha thanks

Answer 9

You're welcome.

Answer 10

Any tips for the SAT

Answer 11

I'm actually taking an SAT course at MIT right now and I haven't taken the SAT yet, so I'm not experience to be talking about that at the moment. Sorry!

Answer 12

Oh no way ! That's awesome!

Answer 13

Thanks a lot!

Answer 14

You plan on going to MIT

Answer 15

It's my dream.

Answer 16

Best of luck to you :)

Answer 17

Thanks a lot. Best of luck to you too for your dreams! :)