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 ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{71}{73}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{36}{71}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{71}{72}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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,
$\frac{2 x^{2} + y^{2}}{2 x^{2} - y^{2}} = \frac{72 + 1}{72 - 1} = \frac{73}{71}$

Suggest Corrections

Similar questions

Q. Find the equation of the circle which cuts the following circles orthogonally.
(i)

x^{2} + y^{2} + 4 x - 7 = 0

2 x^{2} + 2 y^{2} + 3 x + 5 y - 9 = 0

x^{2} + y^{2} + y = 0

$I f 2 x^{2} - 3 x y + y^{2} + x + 2 y - 8 = 0 t h e n \frac{d y}{d x} =$

Q. Find the coordinates of the centre and radius of each of the following circles:
(i) x² + y² + 6x − 8y − 24 = 0
(ii) 2x² + 2y² − 3x + 5y = 7
(iii) 1/2 (x² + y²) + x cos θ + y sin θ − 4 = 0
(iv) x²+ y² − ax − by = 0

Q. If

y = 2 x + K

is a diameter to the circle

2 (x^{2} + y^{2}) + 3 x + 4 y - 1 = 0

, then

K

equals

Q. Solve the following equations:

2 x^{2} - x y + y^{2} = 2 y, 2 x^{2} + 4 x y = 5 y

Join BYJU'S Learning Program

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 ]