20
If x4 + (1/x4) = 34, then what is the value of x3 – (1/x3)?
- A0
- B6
- C8
- D14
Answer not set
Discussion 1
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CCommunity
Given x4 + (1/x4) = 34
Adding 2 to both sides
⇒ x4 + (1/x4) + 2 = 34 + 2
⇒ {x2 + (1/x2)}2 = 62
⇒ x2 + (1/x2) = 6 ……(i)
Subtracting 2 from both sides
⇒ x2 + (1/x2) – 2 = 6 – 2
⇒ (x – 1/x)2 = 22
⇒ x – 1/x = 2 ……(ii)
since we know that x3 – (1/x3) = (x – 1/x) (x2 + 1/x2 + 1) from (i) and (ii)
⇒ x3 – (1/x3) = (2)(6 + 1)
∴ x3 – (1/x3) = 14
Adding 2 to both sides
⇒ x4 + (1/x4) + 2 = 34 + 2
⇒ {x2 + (1/x2)}2 = 62
⇒ x2 + (1/x2) = 6 ……(i)
Subtracting 2 from both sides
⇒ x2 + (1/x2) – 2 = 6 – 2
⇒ (x – 1/x)2 = 22
⇒ x – 1/x = 2 ……(ii)
since we know that x3 – (1/x3) = (x – 1/x) (x2 + 1/x2 + 1) from (i) and (ii)
⇒ x3 – (1/x3) = (2)(6 + 1)
∴ x3 – (1/x3) = 14