Question

Ex.7. If (4x2 - 3y2):(2x2 +5y2)=12:19, then x:y = ?
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Answer 1

Hey mate here is your answer:

$\frac{4x {}^{2} - 3y {}^{2} }{2x {}^{2} + 5y {}^{2} } = \frac{12}{19}$

Applying componendo and dividendo on both the side:

$= > \frac{4x {}^{2} - 3y {}^{2} + 2x {}^{2} + 5y {}^{2} }{4x {}^{2} - 3y {}^{2} - 2x {}^{2} - 5y {}^{2} } = \frac{12 + 19}{12 - 19}$

$\frac{6x {}^{2} + 2y {}^{2} }{2x {}^{2} - 8y {}^{2} } = \frac{31}{ - 7}$

$= > - 7(6x {}^{2} + 2y {}^{2}) = 31(2x {}^{2} - 8y {}^{2} )$

$- 42x {}^{2} - 14y {}^{2} = 62x {}^{2} - 248y {}^{2}$

$= > - 42 x {}^{2} - 62x {}^{2} = - 248y {}^{2} +14y {}^{2}$

$= > - 104x {}^{2} = - 234y {}^{2}$

$= > ( \frac{x}{y} ) {}^{2} = \frac{234}{104}$

$(\frac{x}{y} ) {}^{2} = \frac{225}{100}$

Taking square root on both the sides:

$= > \frac{x}{y} = \frac{15}{10}$

Therefore,x:y=3:2