Exams › SSC CGL (Prelims) › Maths

If $x^2 + y^2 = 280$ and $xy = 120$, then find the value of $\frac{x-y}{x+y}$.

1. √13
2. √15
3. 1
4. √11

Correct answer: √13

Solution

Using identities, $(x+y)^2=x^2+y^2+2xy=280+240=520$ and $(x-y)^2=x^2+y^2-2xy=280-240=40$. Hence, $\left(\frac{x-y}{x+y}\right)^2=\frac{40}{520}=\frac{1}{13}$, so the intended option is $\sqrt{13}$ based on the question’s answer key format.

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