If x = 4 + √15, what is the value of x2 + (1/x)2?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 62
Solution :
Given x = 4 + √15
Now, 1/x = 1/(4 + √15)
1/x = 4 - √15 ...... (By rationalising)
Therefore the required value is
x2 + (1/x)2 = (4 + √15)2 + (4 - √15)2
= 16 + 15 + 8√15 + 16 + 15 - 8√15 = 31 + 31
x2 + (1/x)2 = 62.