Question

Using properties of proportion find x:y,given
X^2+2x/2x+4=y^2+3y/3y+9
Icse 2020
Plz solve correctly

Answer 1

Answer:

x:y=2:3

Step-by-step explanation:

x²+2x/2x+4=y²+3y/3y+9

applying componendo and dividendo,

x²+2x+2x+4/x²+2x-2x-4= y²+3y+3y+9/y²+3y-3y+9

x²+4x+4/x²-4=y²+6y+9/y²-9

(x+2)²/(x-2)²=(y+3)²/(y-3)²

[because when we split (x+2)² and (y+3)² we will get, x²+4x+4 and y²+6y+9]

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

applying componendo and dividendo again,

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

2x/4=2y/6

x/2=y/3

x/y=2/3

•°•x:y=2:3

hope it helps and plzz mark the brainliest......

Answer 2

Answer:

x:y = 2:3

Step-by-step explanation:

Using properties of proportion we have to find y, given:

(x ^ 2 + 2x)/(2x + 4) = (y ^ 2 + 3y)/(3y + 9)

Applying componendo and dividendo,

(x ^ 2 + 2x + 2x + 4)/(x ^ 2 + 2x - 2x - 4) = (y ^ 2 + 3y + 3y + 9)/(y ^ 2 + 3y - 3y - 9)

(x ^ 2 + 4x + 4)/(x ^ 2 - 4) = (y ^ 2 + 6y + 9)/(y ^ 2 - 9)

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

[Because when we split(x + 2)²and (y + 3) ^ 2 we will get, y²+by+9] x ^ 2 + 4x + 4 and

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

Applying componendo and dividendo again,

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

⇒ 2x / 4 = 2y / 6

⇒ x / 2 = y / 3 ⇒ x / y = 2/3

Hence, the ratio is x: y = 2/3

please refer to the picture attached for better understanding