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Home » Thus, there are \(\boxed33\) terms before the value exceeds 100. - American Beagle Club

Thus, there are \(\boxed33\) terms before the value exceeds 100. - American Beagle Club

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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\left( x + rac{1}{x}
ight)^2 = 3^2
\Rightarrow x^2 + 2 + rac{1}{x^2} = 9
\Rightarrow x^2 + rac{1}{x^2} = 7
Next, square this new result to find $ x^4 + rac{1}{x^4} $:
\left( x^2 + rac{1}{x^2}
ight)^2 = 7^2
\Rightarrow x^4 + 2 + rac{1}{x^4} = 49
\Rightarrow x^4 + rac{1}{x^4} = 47
Thus, the value is $ oxed{47} $.

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