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Home » Therefore, the maximum value is \(\boxed2\). - ToelettAPP

Therefore, the maximum value is \(\boxed2\). - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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oxed{\sqrt{7}}
Question: If $x + rac{1}{x} = 4$, what is the value of $x^2 + rac{1}...
Solution: Start with the identity:
\left(x + rac{1}{x}
ight)^2 = x^2 + 2 + rac{1}{x^2}
Substitute $x + rac{1}{x} = 4$:
4^2 = x^2 + 2 + rac{1}{x^2} \Rightarrow 16 = x^2 + rac{1}{x^2} + 2
Solve for $x^2 + rac{1}{x^2}$:
x^2 + rac{1}{x^2} = 16 - 2 = 14
oxed{14}

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