Solve for real numbers: { ((−a^1 −b^2 −c^3 =2024^(12) )),((−a^(−1) −b^(−2) −c^(−3) =2024^(−12) )),((a^1 b^2 c^3 =2024^(24) )) :}


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Question Number 138827 by mathdanisur last updated on 18/Apr/21
$Solve for real numbers: { ((−a^1 −b^2 −c^3 =2024^(12) )),((−a^(−1) −b^(−2) −c^(−3) =2024^(−12) )),((a^1 b^2 c^3 =2024^(24) )) :}$
$S o l v e f o r r e a l n u m b e r s :$ ${\begin{cases} - a^{1} - b^{2} - c^{3} = 2024^{12} \\ - a^{- 1} - b^{- 2} - c^{- 3} = 2024^{- 12} \\ a^{1} b^{2} c^{3} = 2024^{24} \end{cases}$
	Answered by MJS_new last updated on 18/Apr/21

	$- a - b^{2} - c^{3} = p$ $- \frac{1}{a} - \frac{1}{b^{2}} - \frac{1}{c^{3}} = \frac{1}{p}$ ${a b}^{2} c^{3} = p^{2}$ $easy to solve, I get$ $a = - \sqrt{p} \land b = \sqrt[4]{p} \land c = - \sqrt[3]{p}$ $p = 2024^{12}$ $\Rightarrow$ $a = - 2024^{6} \land b = 2024^{3} \land c = - 2024^{4}$
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