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ICSE Class X Math 2014 Paper

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If   x2+y2x2−y2=  178\; \frac{x^2+y^2}{x^2-y^2} = \; \frac{17}{8}, then find the value of:
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Question : 23 of 52
Marks: +1, -0
x:yx: y
Solution:  
Given :x2+y2x2−y2=178: \frac{x^2+y^2}{x^2-y^2}= \frac{17}{8}
Applying componendo and dividendo
  (x2+y2)+(x2−y2)(x2+y2)−(x2−y2)  =17+817−8\; \frac{(x^2+y^2)+(x^2-y^2)}{(x^2+y^2)-(x^2-y^2)} \;= \frac{17+8}{17-8}
⇒    2x22y2  =259\Rightarrow \;\; \frac{2x^2}{2y^2} \;= \frac{25}{9}
⇒    x2y2  =259\Rightarrow \;\; \frac{x^2}{y^2} \;= \frac{25}{9}
⇒    xy  =53\Rightarrow \;\; \frac{x}{y} \;= \frac{5}{3}
⇒  x:y  =5:3.\Rightarrow \;x: y \;=5: 3 .
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