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Given that $$(m+n+p)(mn+mp+np)=25$$ and that $$m^2(n+p)+n^2(m+p)+p^2(m+n)=4$$ for real numbers $m$, $n$, and $p$, what is the value of $mnp$?

 Jun 23, 2019
 #1
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(m + n + p)(mn + mp + np)  = 25

m^2n + mn^2 + mnp + m^2p + mnp + mp^2 + mnp+ n^2p + np^2  = 25

[m^2(n + p) +   n^2(m + p) + p^2(m + n)]  + 3(mnp)  = 25

4 + 3mnp  = 25

3mnp =21

mnp  = 7

 

 

 

cool cool cool     

 Jun 24, 2019

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