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
संबंधित प्रश्न
If x and y both are positive and (2x2 – 5y2) : xy = 1 : 3, find x : y.
Find the ratio between 3.5 m, 475 cm and 2.8 m
Find:
The sub-triplicate ratio of the sub-duplicate ratio of 729x18: 64y6.
Find: The reciprocal ratio of 8: 15.
The ratio between two quantities is 3:4. If the first number is 810, find the second number.
Find the mean proportional between 0.6 and 9.6
Do the ratios 2 kg : 80 kg and 25 g : 625 g form a proportion?
Find the following ratio in the simplest form:
1.8 kg to 6 kg
Akilan walks 10 km in an hour while Selvi walks 6 km in an hour. Find the simplest ratio of the distance covered by Akilan to that of Selvi.
Of the 288 persons working in a company, 112 are men and the remaining are women. Find the ratio of the number of women to the total number of persons.
