Advertisements
Advertisements
प्रश्न
If y is the mean proportional between x and z, show that :
xyz (x+y+z)3 =(xy+yz+xz)3
उत्तर
Since y is the mean proportion between x and z
y2 = xz
LHS
xyz (x + y + z)3
= yy2 (x + y + z)3
= y3 (x + y +z)3
= [y (x + y + z)]3
= (xy + y2 + yz)3
= (xy + y2 + yz)3 = RHS
LHS = RHS
APPEARS IN
संबंधित प्रश्न
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
If a, b, c and d are in proportion prove that `(13a + 17b)/(13c + 17d) = sqrt((2ma^2 - 3nb^2)/(2mc^2 - 3nd^2)`
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)`
Find two numbers such that the mean proportional between them is 14 and third proportional to them is 112.
Find the third proportional to `5(1)/(4) and 7.`
The cost of 4 dozen bananas is Rs 104. How many bananas can be purchased for Rs 6.50?
Are the following statements true?
40 persons : 200 persons = ₹ 15 : ₹ 75
The mean proportional between 4 and 9 is ______.
If x, 2, 10 and y are in continued proportion, the values of x and y are respectively:
The table, given below, shows the values of x and y, where x is proportional (directly proportional) to y.
| x | A | 24 | 15 |
| y | 12 | B | 20 |
The values of A and B are:
