If $$x^4 + x^{-4} = 2207, (x > 0)$$ then the value of $$x + x^{-1}$$ is:
$$x^4 + x^{-4} = 2207$$
$$(x^2 + x^{-2})^2$$ - 2$$(x^2)(x^{-2})$$ = 2207
$$(x^2 + x^{-2})^2$$ - 2 = 2207
$$(x^2 + x^{-2})^2$$ = 2209
Square root of both sides,
$$(x^2 + x^{-2})$$ = 47
Again,
$$(x + x^{-1})^2$$ -Â 2$$(x^1)(x^{-1})$$ = 47
$$(x + x^{-1})^2$$ - 2 =47
$$(x + x^{-1})^2$$ = 49
Square root of both sides,
$$(x + x^{-1})$$ = 7
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