If x⁸ - 433x⁴ + 16 = 0, x > 0, then what is the value of (x+2/x) ?

If x⁸ - 433x⁴ + 16 = 0, x > 0, then what is the value of…

If x⁸ - 433x⁴ + 16 = 0, x > 0, then what is the value of $(x+\frac{2}{x})$ ?

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Correct answer: C

Explanation

The correct answer is Option 3 i.e 5.

Given that, x⁸ - 433x⁴ + 16 = 0

On dividing LHS and RHS by x⁴ one gets,

⇒ x⁴ - 433 + 16/x⁴ = 0

⇒ x⁴ + 16/x⁴ = 433

⇒ x⁴ + 16/x⁴ + 8 = 433 + 8

⇒ (x² + 4/x²)² = 441

⇒ x² + 4/x² = 21

⇒ x² + 4/x² + 4 = 21 + 4

⇒ (x + 2/x)² = 25

⇒ (x + 2/x) = 5