1.

X4 + X-4 = 194, X > 0, then what is the value of \(X + \frac{1}{X} + 2\) ?1. 142. 43. 84. 6

Answer» Correct Answer - Option 4 : 6

Given:

X4 + 1/X4 = 194

Concept used:

(a + b)2 = a2 + b2 + 2ab

Calculation:

X4 + 1/X4 = 194

⇒ (X2)2 + 1/(X2)2 = 194

⇒ (X2)2 + 1/(X2)2 + 2 = 194 + 2                     [Adding 2 both sides]

⇒ (X2)2 + 1/(X2)2 + 2 × X2 × 1/X2 = 196

⇒ (X2 + 1/X2)2 = 196

⇒ X2 + 1/X2 = √196

⇒ X2 + 1/X2 = 14

⇒ X2 + 1/X2 + 2 = 14 + 2                                [Adding 2 both sides]

⇒ X2 + 1/X2 + 2 × X × 1/X = 16

⇒ (X + 1/X)2 = 16

⇒ X + 1/X = √16

⇒ X + 1/X = 4

X + 1/X + 2 = 4 + 2

⇒ X + 1/X + 2 = 6

∴ The value of X + 1/X + 2 is 6.


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