Question

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

Answer 1

Answer: The Correct Answer is 2:3

Step-by-step explanation:

Using the componendo and dividendo rule,

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

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(x+2)^3/(x-2)^3 = (y+3)^3/(y-3)^3

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take cube root on both sides we get

(x+2)/(x-2) = (y+3)/(y-3)

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Again applying componendo and dividendo rule,

(x+2+x-2)/(x+2-x+2) = (y+3+y-3)/(y+3-y+3)

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= 2x/4 = 2y/6

X/2= y/3

x/y = 2/3

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Therefore x:y = 2:3