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Home » Style Like a Pro: Must-Have Resort Wear That’s All the Buzz This Season - Carbonext

Style Like a Pro: Must-Have Resort Wear That’s All the Buzz This Season - Carbonext

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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The expanded form is \(\boxed{x^2 - x - 20}\).
Compute the square of \( (3x - 2) \).
Use the formula \((a - b)^2 = a^2 - 2ab + b^2\):
\[(3x - 2)^2 = (3x)^2 - 2(3x)(2) + (2)^2.\]
\[ = 9x^2 - 12x + 4. \]
The square of \( (3x - 2) \) is \(\boxed{9x^2 - 12x + 4}\).**Question:
Given the function \( h(x) = \frac{3x + 5}{\sqrt{2x + 1}} \), rational...
To rationalize the denominator of \( h(x) = \frac{3x + 5}{\sqrt{2x + 1...
h(x) = \frac{3x + 5}{\sqrt{2x + 1}} \cdot \frac{\sqrt{2x + 1}}{\sqrt{2...
The rationalized form is:

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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...
f(s) = \left( \frac{2s}{s^2 - 1} \right)^2
We minimize $ f(s) $ on $ (1, \sqrt{2}) $.

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