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 – 13x + 40 = 0
II. y^2 – 17y + 72 = 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 – 13x + 40 = 0
II. y^2 – 17y + 72 = 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 – 13x + 40 = 0 => (x – 5)(x – 8) = 0 => x = 5, 8.
Equation II: y^2 – 17y + 72 = 0 => (y – 8)(y – 9) = 0 => y = 8, 9.
Comparing values:
– When x = 5: 5 < 8 and 5 < 9 => x < y
- When x = 8: 8 = 8 and 8 < 9 => x <= y
Thus, x <= y.
समीकरण I: x^2 – 13x + 40 = 0 => x = 5, 8।
समीकरण II: y^2 – 17y + 72 = 0 => y = 8, 9।
तुलना:
– x = 5 < 8, 9
- x = 8 = 8, 8 < 9
अतः, x <= y।