Question

Using Componendo-Dividendo
Find x:y

x^3 + 12x/6x^2+8 = y^3 + 27y/9y^2+ 27​

Answer 1

Answer:

2:3

Step-by-step explanation:

x^3+12x/6x^2+8=y^3+27y/9y^2+27

by using componendo dividendo

$\frac{x^3+12x+6x^2+8}{x^3+12x-6x^2-8}$ =$\frac{ y^3+27y+9y^2 +27}{y^3+27y-9y^2-27}$

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

so x+2/x-2=y+3/y-3

again applying componendo dividendo  

we get,

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

2x/4=2y/6

x/2=y/3

so,x/y=2/3    

:)