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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 : 24 of 52
Marks: +1, -0
x3+y3x3−y3\frac{x^3+y^3}{x^3-y^3}
Solution:  
As xy=53\frac{x}{y}=\frac{5}{3}
Cubing both sides, we get
x3y3=(5)3(3)3=12527\frac{x^3}{y^3}=\frac{(5)^3}{(3)^3}=\frac{125}{27}
Applying componendo and Dividendo
x3+y3x3−y3=125+27125−27\frac{x^3+y^3}{x^3-y^3}=\frac{125+27}{125-27}
⇒x3+y3x3−y3=15298\Rightarrow \frac{x^3+y^3}{x^3-y^3}=\frac{152}{98}
⇒x3+y3x3−y3=7649\Rightarrow \frac{x^3+y^3}{x^3-y^3}=\frac{76}{49}
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