De^� terminer a, b et c trois termes conse^� quences d′une suite ge^� ometrique tels que: { ((a+b+c=36,75)),((abc=343)) :}


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Question Number 185625 by LEKOUMA last updated on 24/Jan/23
$De^� terminer a, b et c trois termes conse^� quences d′une suite ge^� ometrique tels que: { ((a+b+c=36,75)),((abc=343)) :}$
$D \overset{´}{e t e r m i n e r} a, b e t c t r o i s t e r m e s c o n s \overset{´}{e q u e n c e s}$ $d^{'} u n e s u i t e g \overset{´}{e o m e t r i q u e} t e l s q u e :$ ${\begin{cases} a + b + c = 36, 75 \\ a b c = 343 \end{cases}$
	Answered by mr W last updated on 24/Jan/23

	$a = \frac{b}{r}, c = b r$ $a b c = b^{3} = 343 \Rightarrow b = 7$ $\frac{7}{r} + 7 + 7 r = 36.75$ $r^{2} - 4.25 r + 1 = 0$ $r = \frac{4.25 \pm 3.75}{2} = 4 o r \frac{1}{4}$ $(a, b, c) = (28, 7, \frac{7}{4}) o r (\frac{7}{4}, 7, 28)$
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