If 4x-5y3x-y-1- then 2x2-y22x2-y2-1 Mark -

Given nbsp; 4x 5y3x+y=1⇒ 4x 5y=3x+y ⇒ x 6y⇒xy=6⇒x^2y^2=36 2x^2y^2=721 Now, by using componendo and dividendo, we get, 2x^2+y^22x^2 y^2=72+172 1=7371 ...

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Standard IX

Mathematics

Ratio and Proportion

If 4x-5y3x+y=...

Question

$If \frac{4 x - 5 y}{3 x + y} = 1, then \frac{2 x^{2} + y^{2}}{2 x^{2} - y^{2}} =$

[1 Mark ]

\frac{73}{71}

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\frac{71}{73}

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\frac{36}{71}

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\frac{71}{72}

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Solution

The correct option is A $\frac{73}{71}$
Given
$\frac{4 x - 5 y}{3 x + y} = 1 \Rightarrow 4 x - 5 y = 3 x + y$
$\Rightarrow x - 6 y \Rightarrow \frac{x}{y} = 6 \Rightarrow \frac{x^{2}}{y^{2}} = 36$
$\frac{2 x^{2}}{y^{2}} = \frac{72}{1}$
Now, by using componendo and dividendo, we get,
$\frac{2 x^{2} + y^{2}}{2 x^{2} - y^{2}} = \frac{72 + 1}{72 - 1} = \frac{73}{71}$

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If 4x−5y3x+y=1,then 2x2+y22x2−y2= [1 Mark ]

The correct option is A 7371Given 4x−5y3x+y=1⇒4x−5y=3x+y ⇒x−6y⇒xy=6⇒x2y2=36 2x2y2=721 Now, by using componendo and dividendo, we get, 2x2+y22x2−y2=72+172−1=7371

$If \frac{4 x - 5 y}{3 x + y} = 1, then \frac{2 x^{2} + y^{2}}{2 x^{2} - y^{2}} =$

[1 Mark ]