Question : If 5x + 3y = 15 and 2xy = 6, then the value of 5x – 3y is:
Option 1: $3\sqrt{3}$
Option 2: $3\sqrt{5}$
Option 3: $3\sqrt{2}$
Option 4: $3\sqrt{4}$
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Correct Answer: $3\sqrt{5}$
Solution : Given: 2xy = 6 ⇒ xy = 3 5x + 3y = 15 Squaring both sides, ⇒ 25x 2 + 9y 2 + 30xy = 225 Subtracting 60xy from both sides, we get, ⇒ 25x 2 + 9y 2 – 30xy = 225 – 60xy ⇒ (5x – 3y) 2 = 225 – 180 ⇒ (5x – 3y) 2 = 45 ⇒ 5x – 3y = $\sqrt{45}$ ⇒ 5x – 3y = $3\sqrt5$ Hence, the correct answer is $3\sqrt5$.
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