If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P²) + (1/Q²) ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 ie 194.
P = 7 + 4√3, PQ = 1, So, Q = 1 / (7 + 4√3)
On rationalizing,
Q = 7 - 4√3
= (1/P²) + (1/Q²)
= (P² + Q²) / (PQ)²
= [(P + Q)² - 2PQ] / (PQ)²
= [(14)² - 2 × 1] / 1²
= 194