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Home » Fonction quadratique \( P(x) = -2x^2 + 120x - 1000 \). - AMAZONAWS

Fonction quadratique \( P(x) = -2x^2 + 120x - 1000 \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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Question: If $x + y = 10$ and $x^2 + y^2 = 58$, find $x^3 + y^3$.
$x + y = 10$
$x^2 + y^2 = 58$
We first find $xy$ using the identity:
Now substitute into the identity for $x^3 + y^3$:
x^3 + y^3 = (x + y)^3 - 3xy(x + y) = 10^3 - 3 \cdot 21 \cdot 10 = 1000...
oxed{370}
Question: If $x + rac{1}{x} = 3$, what is the value of $x^3 + rac{1}...
x^3 + rac{1}{x^3} = \left(x + rac{1}{x}
ight)^3 - 3\left(x + rac{1}{x}

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باستخدام متطابقة الزاوية المزدوجة، $\cos 2z = 1 - 2\sin^2 z$, تصبح الم...
- 2\sin^2 z = \sin z \implies 2\sin^2 z + \sin z - 1 = 0
لنفترض $u = \sin z$, إذن:
2u^2 + u - 1 = 0 \implies u = \frac{-1 \pm \sqrt{1 + 8}}{4} = \frac{-1...
إذن، $u = \frac{1}{2}$ أو $u = -1$.
لـ $\sin z = \frac{1}{2}$:
z = 30^\circ \quad \text{أو} \quad z = 150^\circ
لـ $\sin z = -1$:
z = 270^\circ
وبالتالي، الحلول في $[0^\circ, 360^\circ]$ هي:

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