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Résoudre à l’aide de la formule quadratique : - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Solution: Let the four terms be $ a - \frac{3d}{2},\ a - \frac{d}{2},\...
\left(a - \frac{3d}{2}\right)^2 + \left(a + \frac{3d}{2}\right)^2 = 2a...
The sum of all four terms is:
The square of the sum is $ (4a)^2 = 16a^2 $.
2a^2 + \frac{9d^2}{2} = 16a^2
\Rightarrow \frac{9d^2}{2} = 14a^2
\Rightarrow d^2 = \frac{28a^2}{9}.
The third term is $ a + \frac{d}{2} $, and the first term is $ a - \fr...

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Question: A materials scientist is analyzing the stiffness of a compos...
Find the minimum value of this expression for $ x \in \left(0, \frac{\...
Recall identities:
\sec^2 x = 1 + \tan^2 x,\quad \csc^2 x = 1 + \cot^2 x
Now, note that:
\tan x + \cot x = \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} = \fra...
But it’s simpler to minimize directly:
Let $ s = \sin x + \cos x $, $ p = \sin x \cos x $. Then:
s^2 = 1 + 2p \Rightarrow p = \frac{s^2 - 1}{2}
We minimize this expression for $ s \in (\sqrt{2}, \sqrt{2}] $, since...

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