Question

If 5x=4y then find the value of the ratio 3x² + y²/3x² - y²​

Answer 1

Step-by-step explanation:

5x=4y

x=4y/5

[3(4y/5)^2 + y^2]

[3(4y/5)^2 - y^2]

3×16y^2 +y^2

25

_____________

3×16y^2 -y^2

25

48y^2+25y^2

____________

48y^2-25y^2

73y^2

_____

23y^2

73

23

Answer 2

Given,

5x = 4y.

To Find,

The value of the expression, $3x^{2} +\frac{y^{2} }{3x^{2} } -y^{2}$.

Solution,

As given, 5x=4y.

So we can say x= $\frac{4y}{5}$.

⇒$x^{2} =(\frac{4y}{5} )^{2}$

⇒3$x^{2}$=3×$\frac{16y^{2} }{25}$.

⇒3$x^{2}$=$\frac{48y^{2} }{25}$.

So,

$3x^{2} +\frac{y^{2} }{3x^{2} } -y^{2}$

=$\frac{48y^{2} }{25}$+$\frac{y^{2} }{\frac{48y^{2} }{25} }$-$y^{2}$.

=$\frac{48y^{2} }{25}$-$y^{2}$+$\frac{25}{48}$.

=$\frac{48y^{2} -25y^{2} }{25}$+$\frac{25}{48}$.

=$\frac{23y^{2} }{25}$+$\frac{25}{48}$.

=$\frac{23y^{2}.48+625 }{25.48}$

$\frac{1104y^{2}+625 }{1200}$.

Hence, the value of  $3x^{2} +\frac{y^{2} }{3x^{2} } -y^{2}$ is  $\frac{1104y^{2}+625 }{1200}$.