Question : If $x^2+y^2=427$ and $xy=202$, then find the value of $\frac{x+y}{x-y}$.
Option 1: $\sqrt{\frac{835}{23}}$
Option 2: $\sqrt{\frac{830}{29}}$
Option 3: $\sqrt{\frac{831}{23}}$
Option 4: $\sqrt{\frac{830}{23}}$
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Correct Answer: $\sqrt{\frac{831}{23}}$
Solution : Given: $x^2+y^2=427$ and $xy=202$. Now, $(x+y)^2=x^2+y^2+2xy$ ⇒ $(x+y)^2=427+2×202$ ⇒ $(x+y)=\sqrt{831}$ ---------------------------------------(1) Also, $(x-y)^2=x^2+y^2-2xy$ ⇒ $(x-y)^2=427-2×202$ ⇒ $(x-y)= \sqrt{23}$ ------------------------------------(2) So, $\frac{x+y}{x-y}$ $= \frac{\sqrt{831}}{\sqrt{23}}$ $= \sqrt{\frac{831}{23}}$. Hence, the correct answer is $\sqrt{\frac{831}{23}}$.
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