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3 years ago

I have a problem can you help me on it its math its select the difference of (2x^2 -13x+7)-(1-12x)= this is were I have my probl

ems can you help me

Mathematics

1 answer:

Finger [1]3 years ago

6 0

$(2x^2 -13x+7)-(1-12x)=\\
2x^2-13x+7-1+12x=\\
2x^2-x+6$

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$x_1+x_2+x_3+...+x_{n-1}+x_n+x_{n+1}=m\\\\
x_1+(x_2'+1)+(x_3'+1)+...+(x_{n-1}'+1)+x_n+x_{n+1}=m\\\\
x_1+x_2'+x_3'+...+x_{n-1}'+x_n+x_{n+1}=m-(n-1)\\\\
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We obtained a linear problem of non-negative integer solutions in (ii). The number of solutions to this type of problem are known: $\dfrac{[(n)+(m-n+1)]!}{(n)!(m-n+1)!}=\dfrac{(m+1)!}{n!(m-n+1)!}$

[I can write the proof if you want]

Now, we just have to calculate the number of forms to permute the men that are dispposed in the row: $m!$

Multiplying all results:

$n!\times\dfrac{(m+1)!}{n!(m-n+1)!}\times m!\\\\
\boxed{\boxed{\dfrac{m!(m+1)!}{(m-n+1)!}}}$

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3 years ago