If x2 - 2√(5x) + 1 = 0, then what is the value of x5 + (1/x5)?
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Correct answer: C
Explanation
The correct answer is option 3 i.e 610√5
⇒ x2 - 2√(5x) + 1 = 0
⇒ (x - √5 + 4)(x - √5 - 4)
⇒ x + 1 / x = √5 + 4 + √5 - 4
⇒ 2√5
⇒ x2 + 1 / x2 = (x + 1 / x)2 - 2
⇒ x2 + 1 / x2 = 20 - 2 = 18
⇒ x3 + 1 / x3 = (x + 1 / x)3 - 3(x + 1 /x)
⇒ 40√5 - 3 × 2√5
⇒34√5
x5 + 1 / x5 = (x2 + 1 / x2)(x3 + 1 / x3) - (x + 1 / x)
⇒ 18 × 34√5 - 2√5
⇒ 610√5