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Home » Contradiction. Hence, no such vector $\mathbfw$ exists. - 500apps

Contradiction. Hence, no such vector $\mathbfw$ exists. - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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\left(x + \frac{1}{x}\right)^2 = 4^2 = 16
\Rightarrow x^2 + 2 + \frac{1}{x^2} = 16
\Rightarrow x^2 + \frac{1}{x^2} = 14
Now multiply both sides by 5:
5x^2 + \frac{5}{x^2} = 5 \times 14 = 70
Thus, the value is $ \boxed{70} $.
Question: Compute the square of $ \sqrt{7 + 2\sqrt{10}} + \sqrt{7 - 2\...
Solution: Let $ x = \sqrt{7 + 2\sqrt{10}} + \sqrt{7 - 2\sqrt{10}} $. W...
x^2 = \left( \sqrt{7 + 2\sqrt{10}} + \sqrt{7 - 2\sqrt{10}} \right)^2 =...
x^2 = 14 + 2\sqrt{7^2 - (2\sqrt{10})^2} = 14 + 2\sqrt{49 - 40} = 14 +...

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