If (a+1over a)=7sqrt3 , then what is the value of (a⁶ + a⁻⁶)?

If (a+1over a)=7sqrt3 , then what is the value of (a⁶ +…

If $(a+{1\over a})=7\sqrt3$ , then what is the value of (a⁶ + a^-6)?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 3048190.

If x + (1/x) = a then x² + 1/x² = a² - 2 and x³ + 1/x³ = a³ - 3a

$(a+{1\over a})=7\sqrt3$

⇒ $(a^2+{1\over a^2})=(7\sqrt3)^2-2=145$

⇒ (a²)³ + 1/(a²)³ = (145)³ - 3(145)

⇒ a⁶ + a^-6 = 3048625 - 435 = 3048190

Therefore, the required value is 3048190.