Given \frac{x^3+12 x}{6 x^2+8}=\frac{y^3+27 y}{9 y^2+27} . Using componendo and dividendo find x: y.

ICSE Class X Math 2015 Solved Paper - Question 51

Question : 51 of 52

Marks: +1, -0

Given

\;{x^3+12 x}/{6 x^2+8}=\;{y^3+27 y}/{9 y^2+27} . \;\;

Using componendo and dividendo find

x : y

Solution:

\;{x^3+12 x}/{6 x^2+8}=\;{y^3+27 y}/{9 y^2+27} . \;\;

Applying componendo and dividendo

\;{x^3+12 x+6 x^2+8}/{x^3+12 x-6 x^2-8}\;

=\;{y^2+27 y+9 y^2+27}/{y^3+27 y-9 y^2-27}

\;{(x+2)^3}/{(x-2)^3}\;=\;{(y+3)^3}/{(y-3)^3}

\;{x+2}/{x-2}\;=\;{y+3}/{y-3}

Again, applying componendo and dividendo

\;{x+2+x-2}/{x+2-x+2}\;=\;{y+3+y-3}/{y+3-y+3}

\;{2 x}/{4}\;=\;{2 y}/{6}

\;{x}/{y}\;=\;{4}/{6}=\;{2}/{3}

x: y\;=2: 3 .

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