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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