If x⁸ + 1 over x⁴ = 14, then the value of x¹2 + 1 over x⁶ is:

If x⁸ + 1 over x⁴ = 14, then the value of x¹2 + 1 over x⁶…

If $x^8 + 1 \over x^4$ = 14, then the value of $x^12 + 1 \over x^6$ is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 52

If $x^8 + 1 \over x^4$ = 14

x⁴ + 1/x⁴ = 14

x² + 1/x² = √(14 + 2) = √16 = 4

The value of $x^12 + 1 \over x^6$

x⁶+ 1/x⁶ = (x² + 1/x²)³ - 3 (x² + 1/x²)

= 64 - 3 * 4 = 64 - 12 = 52