If x2 – 16x + 59 = 0, then what is the value of (x – 6)2 + [1/(x – 6)2]?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 18
x2 – 16x + 59 = 0
Let x - 6 = m
x = m + 6
So,
(x – 6)2 + 1/(x – 6)2 = m2 + 1/m2
Now,
(m + 6)2 - 16(m + 6) + 59 = 0
⇒ m2 + 36 + 12m - 16m - 96 + 59 = 0
⇒ m2 - 4m - 1 = 0
Divising by m:
⇒ m - 1/m = 4
⇒ m2 + 1/m2 = (m - 1/m)2 + 2
⇒ (x – 6)2 + 1/(x – 6)2 = 16 + 2 = 18