Question

Please help me with the question provided in the attachment.

No spams please.. /(^_^) ​

Answer 1

step by step ..

1. divide the numerator and denominator by y^3 .

2. let , x/y = k

and the proceed ..

hence , x/y = 3/2 .

there fore , x : y = 3 : 2 .

☺️ keep learning ☺️

Answer 2

Given:

$\frac{x^{3}+4 x y^{2}}{4 x^{2} y+y^{3}}=15 / 16$

To find:

x : y

Solution:

$\begin{aligned}& \frac{x^{3}+4 x y^{2}}{4 x^{2} y+y^{3}}=15 / 16 \\&\frac{(x / y)^{3}+4(x / y)}{4(x / y)^{2}+1}=15 / 6\left[k y x^{3}\right] \\\Rightarrow & \frac{k^{3}+4 k}{4 k^{2}+1}=15 / 16[x / y-k] \\\Rightarrow & 16 k^{3}+64 k=60 k^{2}+15 \\\Rightarrow & 16 k^{3}-60 k^{2}+64 k-15=0 \\\Rightarrow & 16 k^{3}-24 k^{2}-36 k^{2}+54 k+10 k-15=0 \\\Rightarrow & 8 k^{2}(2 k-3)-18 k(2 k-3)+5(2 k-3)=0 \\\Rightarrow &(2 k-3)\left(8 k^{2}-18 k+5\right)=0 \\& 2 k-3=0 \\& k=3 / 2\end{aligned}$

Therefore, x : y = 3 : 2.