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Ronny en Alan

Ronny's leeftijd plus het kwadraat van Alan's leeftijd is 2240. Alan's leeftijd plus het kwadraat van Ronny's leeftijd is 1008. Hoe oud zijn Ronny en Alan?

francine
19-1-2014

Antwoord

$
\begin{array}{l}
\left\{ \begin{array}{l}
r + a^2 = 2240 \\
r^2 + a = 1008 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
r = 2240 - a^2 \\
r^2 + a = 1008 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
r = 2240 - a^2 \\
\left( {2240 - a^2 } \right)^2 + a = 1008 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
r = 2240 - a^2 \\
a^4 - 4480a^2 + 5017600 + a = 1008 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
r = 2240 - a^2 \\
a^4 - 4480a^2 + a + {\rm{5016592}} = 0 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
r = 2240 - a^2 \\
\left( {a - 47} \right)\left( {a^3 + 47a^2 - 2271a - 106736} \right) = 0 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
r = 2240 - a^2 \\
a = 47 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
r = 31 \\
a = 47 \\
\end{array} \right. \\
\end{array}
$

Zoiets?

WvR
19-1-2014