Advertisements
Advertisements
प्रश्न
Find mean proportional of `( x + y)/( x - y), (x^2 - y^2)/(x^2y^2)`
उत्तर
If b is the mean proportional of a and c, then `b^2 = ac`
Mean proportional of `[ x + y]/[ x - y] and [ x^2 - y^2]/[ x^2y^2]`
`therefore b^2 = [x + y]/[x - y] xx [ x^2 - y^2]/[x^2y^2]`
`b^2 = [x + y]/[x -y] xx [( x - y)( x + y)]/( x^2y^2)`
`therefore b^2 = [(x + y)^2]/(xy)^2`
`therefore b = [x + y]/(xy)`
APPEARS IN
संबंधित प्रश्न
if `a/b = c/d` prove that each of the given ratio is equal to: `((8a^3 + 15c^3)/(8b^3 + 15d^3))^(1/3)`
If a, b, c and d are in proportion prove that `sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((xa^3 - 4yb^3)/(xc^3 - 5yd^3))^(1/3)`
If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`
Find the value of the unknown in the following proportion :
`1/2 : "m" :: 14/9 : 4/3`
Find the third proportional to:
x - y, x2 - y2
Find the third proportional to Rs. 3, Rs. 12
What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?
If 22.5 m of a uniform iron rod weighs 85.5 kg, what will be the weight of 5 m of the same rod?
The cost of 18 chairs is Rs 22770. How many such chairs can be bought for Rs 10120?
If a, b, c and d are in proportion, prove that: `(a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)`
