Advertisements
Advertisements
प्रश्न
If `(a + b)^3/(a - b)^3 = 64/27`.
- Find `(a + b)/(a - b)`
- Hence using properties of proportion, find a : b.
उत्तर
a. Given `(a + b)^3/(a - b)^3 = 64/27`
Taking cube root on both sides, we get
`(a + b)/(a - b) = root(3)(64/27)`
`implies (a + b)/(a - b) = 4/3`
b. Now `(a + b)/(a - b) = 4/3`
Applying componendo and dividendo, we get
`((a + b) + (a - b))/((a + b) - (a - b)) = (4 + 3)/(4 - 3)`
`\implies (2a)/(2b) = 7/1`
`\implies a/b = 7/1`
Hence, a : b = 7 : 1
APPEARS IN
संबंधित प्रश्न
Find the third proportional to `2 2/3` and 4
Find the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)`
If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`
If q is the mean proportional between p and r prove that `(p^3 + q^3 + r^3)/(p^2q^2r^2) = 1/p^3 + 1/q^3 = 1/r^3`
Check whether the following numbers are in continued proportion.
1, 2, 3
Find the fourth proportion to the following:
3,5 and 15
If `1/12` , x and `1/75` are in continued proportion , find x.
If 12 L of diesel is consumed by a car in covering a distance of 222 km, how many kilometers will it go in 22 L of diesel?
If the ratios formed using the numbers 2, 5, x, 20 in the same order are in proportion, then ‘x’ is
Write True (T) or False (F) against the following statement:
12 : 18 : : 28 : 12
