x + (1/x) = 2, y - (1/y) = 3 হলে, x² + y² + (1/x²) + (1/y²) এর মান কত?
Solution
Correct Answer: Option D
দেওয়া আছে,
x + (1/x) = 2
⇒ (x + 1/x)² = 2²
⇒ x² + 2 * x * 1/x + (1/x²) = 4
⇒ x² + 2 + (1/x²) = 4
⇒ x² + (1/x²) = 4 - 2
⇒ x² + (1/x²) = 2
আবার,
y - (1/y) = 3
⇒ (y - 1/y)² = 3²
⇒ y² - 2 * y * 1/y + (1/y²) = 9
⇒ y² - 2 + (1/y²) = 9
⇒ y² + (1/y²) = 9 + 2
⇒ y² + (1/y²) = 11
এখন,
x² + y² + (1/x²) + (1/y²) = x² + (1/x²) + y² + (1/y²)
= 2 + 11
= 13