Question : If $x-y=1$ and $x^2+y^2=41$ where $x, y \geq 0$, then the value of $x+y$ will be:
Option 1: 9
Option 2: 8
Option 3: 6
Option 4: 7
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Correct Answer: 9
Solution :
Given: $x-y=1$ and $x^2+y^2=41$
Consider $x-y=1$
Squaring both sides, we get:
⇒ $(x-y)^2 =1$
⇒ $x^2 + y^2 - 2xy=1$
⇒ $41-2xy=1$
⇒ $2xy = 40$
So, $ (x+y)^2 = x^2+y^2+2xy= 41+40$
$\therefore(x+y) = 9$
Hence, the correct answer is 9.
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