Rational rearrangement and a ratio

Rational rearrangement and a ratio

Secondary 2
TGM Original Questions

Positive quantities satisfy \(\frac{p-x}{q}=\frac{p}{p+x}\). Express \(x\) in terms of \(p,q\). Given further that \(p=5q\), find \(x:q\).

Solution:

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Answer:\(x=\sqrt{p(p-q)}\); \(x:q=2\sqrt5:1\).

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