If k4 + (1/k4) = 47, then what is the value of k3 + (1/k3) ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 18.
Formula used:
(a + b)2 = a2 + b2 + 2ab ---- (1)
(a + b)3 = a3+ b3 + 3ab(a + b) ----- (2)
Calculations:
⇒ (k2 + 1/k2)2 = 47 + 2 = 49
⇒ (k2 + 1/k2) = 7
Now, (k + 1/k)2 = 7 + 2 = 9
⇒ (k + 1/k) = 3
using equation (2), we get
⇒ 33 = k3 + 1/k3 + 3 × 3
⇒ k3 + 1/k3 = 27 - 9 = 18