Question : If $x$ and $y$ are positive numbers such that $x - y = 5$ and $xy = 150$, the value of $(x + y)$ is:
Option 1: 45
Option 2: 25
Option 3: 35
Option 4: 15
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Correct Answer: 25
Solution :
Given: $x - y = 5$ and $xy = 150$
Squaring both sides of the given equation $x - y = 5$, we get,
$(x - y)^2 = 5^2$
⇒ $x^2 + y^2 - 2xy = 25$
⇒ $x^2 + y^2 - 2 × 150 = 25$
⇒ $x^2 + y^2 = 325$
So, the value of $(x + y)$ is calculated as,
$(x + y)^2 = x^2 + y^2 + 2xy$
⇒ $(x + y)^2 = 325 + 2 × 150$
⇒ $(x + y)^2 = 625$
⇒ $(x + y) =\sqrt{625}$
⇒ $(x+ y) = 25$
Hence, the correct answer is $25$.
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