Learn how to solve the system for m, n, and p quickly

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Learn how to solve the system for m, n, and p quickly | Math Olympiad Training

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Жыл бұрын

Learn how to solve the given system of equations for m, n, and p in the olympiad question. Step-by-step tutorial by PreMath.com
Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy way. Learn how to prepare for Math Olympiad fast!
Step-by-step tutorial by PreMath.com
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Пікірлер: 22

@wackojacko3962 Жыл бұрын

Classic! 🙂

@PreMath Жыл бұрын

Excellent! Thanks! Cheers!

@misterenter-iz7rz Жыл бұрын

Add all to get 2(p+n+m)=3pmn, subtract two pairs of equations, we get m=n=p, so 6p=3p^3, or p=0 or p=+ or - root 2.😂

@PreMath Жыл бұрын

Excellent! Thank you! Cheers! 😀

@KAvi_YA666 Жыл бұрын

Thanks for video.Good luck sir!!!!!!!!

@PreMath Жыл бұрын

So nice of you, dear You are awesome. Keep it up 👍

@alster724 Жыл бұрын

Very refreshing

@PreMath Жыл бұрын

Thanks

@dirklutz2818 Жыл бұрын

Brilliant

@PreMath Жыл бұрын

Thanks

@brunococchietto7496 Жыл бұрын

It took me about half an hour to find the solution,I must do these things on a daily basis.

@PreMath Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@danieldennis9831 Жыл бұрын

I got p=m= n pretty quick. The 2p=p^3 took time .. But the 2=p^2 got to p=±√2. The p=0 I didn't figure before watching.

@PreMath Жыл бұрын

Bravo! Thanks for sharing! Cheers!

@honestadministrator Жыл бұрын

If p= 0, then m = n = p ( m n -1) = 0 Extension of this argument implies either each number p, m, n are Zero OR none of them are Zero To expire non zero solutions, a bit of work gives 1/(p n) + 1/( m p) = 1 1/(p n) + 1/( m n) = 1 1/(m p) + 1/(m n ) = 1 Hereby 1/(p n) = 1/( m p) = 1/( m n) = 1/2 This implies m = n = p & m^2 = 2 EITHER m = n = p = √2 OR m = n = p = -√2 Hereby set of all feasible solutions are m = n = p = k Wherein k = 0, √2, - √2

@user-jn3qd3xc9w Жыл бұрын

2(m+n+p)=3pmn M+n+p=1.5pmn n=p=m=0.5pmn 2n=n^3 n(n^2-2)=0 n(n-sqrt2)(n+sqrt2)=0 n=0,sqrt2,-sqrt2

@PreMath Жыл бұрын

Excellent! Thank you! Cheers! 😀

@eunkyungyoon4751 9 ай бұрын

classic

@vishwambharmahant9485 Жыл бұрын

M=N=P=PMN/2

@misterenter-iz7rz Жыл бұрын

The second puzzle😅

@PreMath Жыл бұрын

Yes! Thank you! Cheers! 😀

@devondevon4366 Жыл бұрын

Answer p=n=m= 0, sqrt 2, and - sqrt 2 m+ n = n+ p [transitive property, since both equal pmn] m=p [subtract n from both sides] n+p = m+ p [ transitive property] n=m [subtract p from both sides] p=n [transitive property since both =m] p=n=m n+ n = n*n*n {substitute the value of n into any of the three given equations} 2n =n^3 0 = n^3 - 2n 0 = n ( n^2 -2) n=0 n^2 - 2=0 n^2 = 2 n = sqrt 2 and -sqrt 2