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Question Number 184304 by mathlove last updated on 05/Jan/23

	Answered by Frix last updated on 05/Jan/23

	$a = \frac{1 + \sqrt{4 t + 221}}{2}$ $a + \frac{2}{a} = 1 \Leftrightarrow a^{2} - a + 2 = 0 \Leftrightarrow t = - 57$ $P = t^{2} - 1226 = 2023$
	Answered by Rasheed.Sindhi last updated on 05/Jan/23

	$a^{2} - a + 2 = 0 \Rightarrow a^{2} - a = - 2$ $P = ((a + 9) (a - 10) ((a + 4) (a - 5)) - 1$ $= (a^{2} - a - 90) (a^{2} - a - 20) - 1$ $= (- 2 - 90) (- 2 - 20) - 1$ $= (- 92) (- 22) - 1$ $= 2024 - 1 = 2_{0} 2_{3} (H a p p y N e w Y e a r!)$
	Commented by Frix last updated on 05/Jan/23

	$Yes! I was looking for a more complicated$ $approach; -)$
	Commented by Rasheed.Sindhi last updated on 05/Jan/23

	$E x c u s e m e s i r, (1) Y o u r a p p r o a c h$ $i s c o m p l i c a t e d . (2) Y e t y o u r a n s w e r$ $i s t o o s h o r t t o u n d e r s t a n d :)$ $O r$ $I^{'} m n o t s h a r p e n o u g h . . .$
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