If $(2 x^{2} + 3 y^{2}) : (2 x^{2} - 3 y^{2}) = 11 : 5$ , find the value of $(5 x^{4} + 7 y^{4}) : (5 x^{4} - 7 y^{4})$ .

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Solution

The correct option is C

$\frac{2 x^{2} + 3 y^{2}}{2 x^{2} - 3 y^{2}} = \frac{11}{5}$
Using componendo and dividendo
$\frac{(2 x^{2} + 3 y^{2}) + (2 x^{2} - 3 y^{2})}{(2 x^{2} + 3 y^{2}) - (2 x^{2} - 3 y^{2})} = \frac{11 + 5}{11 - 5} \frac{4 x^{2}}{6 y^{2}} = \frac{16}{6} \frac{x^{2}}{y^{2}} = \frac{4}{1} \frac{x^{4}}{y^{4}} = \frac{16}{1}$
Multiplying both sides by $\frac{5}{7}$
$\frac{5 x^{4}}{7 y^{4}} = \frac{80}{7}$
Using componendo and dividendo
$\frac{5 x^{4} + 7 y^{4}}{5 x^{4} - 7 y^{4}} = \frac{87}{73}$

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