Question:
In the following question, two equations numbered I and II are given. Solve both equations and establish the relationship between x and y:
I. x^2 – 9x + 20 = 0
II. y^2 – 11y + 30 = 0
(a) x > y
(b) x <= y
(c) x >= y
(d) x < y
(e) x = y or relationship cannot be established
निम्नलिखित प्रश्न में, दो समीकरण I और II दिए गए हैं। दोनों समीकरणों को हल करें और x और y के बीच संबंध स्थापित करें:
I. x^2 – 9x + 20 = 0
II. y^2 – 11y + 30 = 0
(a) x > y
(b) x <= y
(c) x >= y
(d) x < y
(e) x = y या संबंध स्थापित नहीं किया जा सकता
Correct Answer: (b)
Explanation:
Equation I: x^2 – 9x + 20 = 0 => (x – 4)(x – 5) = 0 => x = 4, 5.
Equation II: y^2 – 11y + 30 = 0 => (y – 5)(y – 6) = 0 => y = 5, 6.
Comparing values:
– x = 4 < y(5, 6)
- x = 5 = y(5) and x = 5 < y(6)
Thus, x <= y.
समीकरण I: x^2 – 9x + 20 = 0 => x = 4, 5।
समीकरण II: y^2 – 11y + 30 = 0 => y = 5, 6।
तुलना: x = 4 < 5, 6; x = 5 = 5 और < 6।
अतः, x <= y।