If x² - 3x + 1 = 0, then the value of 2( x⁸ + 1/(x⁸) ) - 5( x² + 1/(x²) ) is:

If x² - 3x + 1 = 0, then the value of 2( x⁸ + 1/(x⁸) )…

If x² - 3x + 1 = 0, then the value of $2\left( {{x^8} + \frac{1}{{{x^8}}}} \right) - 5\left( {{x^2} + \frac{1}{{{x^2}}}} \right)$ is:

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Correct answer: A

Explanation

The correct answer in option 1 i.e. 4379

If $(x+\frac{1}{x})$ = a, then $(x^2+\frac{1}{x^2})$ = a²- 2

$(x^2+\frac{1}{x^2})$ = 3² - 2 = 7

$(x^4+\frac{1}{x^4})$ = 7² - 2 = 47

$(x^8+\frac{1}{x^8})$ = (47)² - 2 = 2207

$\rm 2(x^8+\frac{1}{x^8}) - 5(x^2+\frac{1}{x^2}) =$ (2 × 2207) - (5 × 7)

=4379