Advertisements
Advertisements
प्रश्न
Given `(x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27)`. Using componendo and dividendo, find x : y.
Advertisements
उत्तर
`(x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27)`
Applying componendo and dividendo, we get
`((x^3 + 12x) + (6x^2 + 8))/((x^3 + 12x) - (6x^2 + 8)) = ((y^3 + 27y) + (9y^2 + 27))/((y^3 + 27y) - (9y^2 + 27))`
`\implies ((x^3 + 12x) + (6x^2 + 8))/((x^3 + 12x) - (6x^2 - 8)) = ((y^3 + 27y) + (9y^2 + 27))/((y^3 + 27y) - (9y^2 - 27))`
`\implies (x^3 + 6x(2 + x) + 2^3)/(x^3 - 6x (x - 2) - 2^3) = ((y^3 + 9y)(y + 3) + 3^3)/((y^3 - 9y) (y - 3) - 3^3)`
`\implies (x + 2)^3/(x - 2)^3 = (y + 3)^3/(y - 3)^3`
Again applying componendo and dividendo, we get
`(x + 2 + x - 2)/(x + 2 - x + 2) = (y + 3 + y - 3)/(y + 3 - y + 3)`
`\implies (2x)/4 = (2y)/6`
`\implies x/2 = y/3`
Applying alternendo, we get
`\implies x/y = 2/3`
∴ x : y = 2 : 3
APPEARS IN
संबंधित प्रश्न
If a: b = 4: 7, find the following:
`(5"a" - 4"b")/(2"a" - 3"b")`
Find the compounded ratio of the following:
15: 16 and 8 : 5
Express the following ratios in its simplest form :
`1 1/2:2 1/2`
Express the given ratio in its simplest form: 6 months: `1 1/3` years
Find the third proportional of 1.6 and 0.8
Find the ratio of the first quantity to the second.
125 cm, 1 metre
From the given pairs, find which ratio is larger:
(3 : 4) or (9 : 16)
10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?
20 m : 70 m = Rs 8 : Rs ______.
A train takes 2 hours to travel from Ajmer to Jaipur, which are 130 km apart. How much time will it take to travel from Delhi to Bhopal which are 780 km apart if the train is travelling at the uniform speed?
