Question

if x/y = 2/3 then 2x² + 3y²/ 2x² - 3y² = ?​

Answer 1

Step-by-step explanation:

$\frac{x}{y} = \frac{2}{3} \\ \\ so \: \: \: x = 2 \: \: \: \: y = 3 \\ \\ hence \: \: \frac{2 {x}^{2} + 3 {y}^{2} }{2 {x}^{2} - 3 {y }^{2} } \\ \\ = \frac{2 \times {2}^{2} + 3 \times {3}^{2} }{2 \times {2}^{2} - 3 \times {3}^{2} } \\ \\ = \frac{2 \times 4 + 3 \times 9}{2 \times 4 - 3 \times 9} \\ \\ = \frac{8 + 27}{8 - 27} = \frac{35}{ - 19} = - \frac{35}{19}$

Answer 2

Given : x/y = 2/3

To Find : 2x² + 3y² / 2x² - 3y²

1️⃣ 35/19

2️⃣ 19/35

3️⃣ -19/35

4️⃣ -35/19​

Solution:

x/y = 2/3

Squaring both sides

=> ( x/y)² = (2/3)²  = 4/9

2x² + 3y² / 2x² - 3y²

Dividing numerator and denominator by y²

= (2( x/y)² + 3) / (2( x/y)²  - 3)

= (2 (4/9) + 3) / (2 (4/9)  - 3)

multiplying numerator and denominator by 9

= ( 8 +  27) / ( 8 - 27)

= 35 / (-19)

= - 35/19

2x² + 3y² / 2x² - 3y²   = -35/19​

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