Question 88

If $$\frac{(5x-y)}{(5x+y)}=\frac{3}{7}$$, then what is the value of $$\frac{4x^{2}+y^{2}-4xy}{9x^{2}+16y^{2}+24xy}$$ ?

Solution

Given : $$\frac{(5x-y)}{(5x+y)}=\frac{3}{7}$$

=> $$35x-7y=15x+3y$$

=> $$35x-15x=7y+3y$$

=> $$20x=10y$$

=> $$\frac{x}{y}=\frac{10}{20}=\frac{1}{2}$$

Let $$x=1$$ and $$y=2$$

To find : $$\frac{4x^{2}+y^{2}-4xy}{9x^{2}+16y^{2}+24xy}$$

= $$\frac{4(1)^2+(2)^2-4(1)(2)}{9(1)^2+16(2)^2+24(1)(2)}$$

= $$\frac{4+4-8}{9+64+48}=0$$

=> Ans - (A)

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