If (x¹² + 1 )/x⁶ = 6, then the value of (x³⁶ + 1 )/x¹⁸ ?
(A) 188
(B) 192
(C) 196
(D) 198


Answer: (D)

Explanation: Given
(x¹² + 1 )/x⁶ = 6
x⁶ + 1 /x⁶ = 6
Cubing both sides
(x⁶ + 1 /x⁶)³ = 6³
x¹⁸ + 1/x¹⁸ + 3 (x⁶ + 1 /x⁶) = 216
x¹⁸ + 1/x¹⁸ + 3 * 6 = 216
x¹⁸ + 1/x¹⁸ = 198
(x³⁶ + 1)/x¹⁸ = 198

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