Question:
The sum of two numbers x and y (where x is greater than y) is equal to four times their difference. Find the value of 5xy / (3(x2 – y2)).
दो संख्याओं x और y (जहाँ x, y से बड़ा है) का योग उनके अंतर के चार गुना के बराबर है। 5xy / (3(x2 – y2)) का मान ज्ञात कीजिए।
Options:
- a) 25/16
- b) 16
- c) 2 3/16
- d) 25
- a) 25/16
- b) 16
- c) 2 3/16
- d) 25
correct answer : a)
Explanation:
Given: x + y = 4(x – y)
⇒ x + y = 4x – 4y
⇒ 5y = 3x
⇒ x / y = 5 / 3.
Let x = 5k and y = 3k.
Then, 5xy / (3(x2 – y2)) = (5 × 5k × 3k) / (3 × ((5k)2 – (3k)2))
= 75k2 / (3 × (25k2 – 9k2))
= 75k2 / (3 × 16k2)
= 25 / 16.
दिया गया है: x + y = 4(x – y)
⇒ x + y = 4x – 4y
⇒ 5y = 3x
⇒ x / y = 5 / 3.
माना x = 5k और y = 3k.
अतः, 5xy / (3(x2 – y2)) = (5 × 5k × 3k) / (3 × ((5k)2 – (3k)2))
= 75k2 / (3 × (25k2 – 9k2))
= 75k2 / (3 × 16k2)
= 25 / 16.