If k2 −2KK+1 = 16 , then what is the value of K1 3 + K3 ? ​ ​ ​

Explanation

Given: K k2 −2 K+1 = 16 ​ ​ Concept Used: If x + 1/x = a, then x3 + 1/x3 = a3 - 3a Calculation: K k2 −2 K+1 = 16 ​ ​ Take K common from numerator and denominator 1 K−2+ K1 ​ ​ = 16 ​ K − 2 + K1 = 6 ​ K + K1 = 8 ​ K 3 + K13 = 83 − 3 × 8 ​ K 3 + K13 = 512 − 24 = 488​ ∴ Option 4 is the correct answer.