CAT 2023 Surds and Indices Question (Hard)

Question

If is a positive real number such that , then the value of is

Accepted Answer

Step 1 Let Try . Then - - - So is valid. --- Step 2 Define recurrence Let Then T_n a cdot T_ n-1 - T_ n-2 Start with - - Compute further terms - - - - - - - --- Final Answer

CAT 2023

Quantitative

Surds and Indices

Hard

If $x$ is a positive real number such that $x^8 + \left(\frac{1}{x}\right)^8 = 47$ , then the value of $x^9 + \left(\frac{1}{x}\right)^9$ is

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