Q-find-the-number-of-the-solutions-for-x-1-x-2-3-x-3-x-4-x-5-11-Hint-x-i-Z-0-

Question Number 189302 by mnjuly1970 last updated on 14/Mar/23

Q : find the number of

the solutions for :

{(x_{1} + x_{2})}^{3} + x_{3} + x_{4} + x_{5} = 11

H i n t : (x_{i} \in Z^{+} \cup {0})

Commented by Frix last updated on 14/Mar/23

Z^{+} \cup {0} = N

Commented by Frix last updated on 14/Mar/23

a^{3} + b = 11

a = 0 \land b = 11

a = 1 \land b = 10

a = 2 \land b = 3

Now {it}^{'} s just counting \dots

Answered by manxsol last updated on 15/Mar/23

a^{3} + b = 11

\begin{array}{cccc} a & b \\ 0 & 11 \\ 1 & 10 \\ 2 & 3 \end{array} x_{c_{}} = \underset{4}{x} + x_{5}

\begin{array}{ccccccc} a & x_{1} & x_{2} \\ 0 & 0 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ 2 & 0 & 2 \\ 2 & 1 & 1 \\ 2 & 2 & 0 \end{array} \begin{array}{ccccccc} b & x_{3} & x_{c} \\ 11 & 11 & 0 \\ 11 & 10 & 1 \\ 11 & 9 & 2 \\ 11 & 0 & 11 \end{array}

{\begin{array}{ccccccccccccccc} x_{c} & x_{4} & x_{5} & ♯ \\ 0 & 0 & 0 & 1 \\ 1 & \begin{array}{cc} 0 \\ 1 \end{array} & \begin{array}{cc} 1 \\ 0 \end{array} & 2 \\ 2 & \begin{array}{ccc} 0 \\ 1 \\ 2 \end{array} & \begin{array}{ccc} 2 \\ 1 \\ 2 \end{array} & 3 \\ 3 & \begin{array}{cccc} 0 \\ 1 \\ 2 \\ 3 \end{array} & \begin{array}{cccc} 3 \\ 2 \\ 1 \\ 0 \end{array} & 4 \\ 4 \\ 5 \\ 6 \\ 7 \\ 8 \\ 9 \\ 10 \\ 11 \\ \sum_{1}^{12} = 78 \end{array}}_{}

\begin{array}{cc} x_{1} x_{2} & x_{3} & x_{4} x_{5} & (x_{\hat{1}} x_{2}, x_{3,}, x_{4}, x_{5} \\ 6 & 12 & 78 & 5616 \end{array}

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