ICSE Class X Math 2014 Solved Paper

If $\;{x^2+y^2}/{x^2-y^2}=\;{17}/{8}$ , then find the value of:

Question : 23 of 52

Marks: +1, -0

x : y

Solution:

Given

: \;{x^2+y^2}/{x^2-y^2}=\;{17}/{8}

Applying componendo and dividendo

\;\;{ (x^2+y^2) + (x^2-y^2) }/{ (x^2+y^2) - (x^2-y^2) }\;=\;{17+8}/{17-8}

⇒\;\;{2 x^2}/{2 y^2}\;=\;{25}/{9}

⇒\;\;{x^2}/{y^2}\;=\;{25}/{9}

⇒\;\;{x}/{y}\;=\;{5}/{3}

⇒\;x: y\;=5: 3 .

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