Advertisements
Advertisements
प्रश्न
If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^2/b^2 + z^3/c^2 = ((x + y + z)^3)/((a + b ++ c)^2)`.
Advertisements
उत्तर
Let `x/a = y/b = z/c = k` ...[By k method]
x = ak, y = bk and z = ck.
L.H.S.
= `(a^3k^3)/(a^2) + (b^3k^3)/(b^2) + (c^3k^3)/(c^2)`
⇒ k3 [a + b + c]
R.H.S.
= `[ak + bk + ck]^3/[a + b + c]^2`
⇒ `(k^3[a + b + c]^3)/[a + b + c]^2`
= k3 (a + b + c)
L.H.S. = R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.
Find mean proportional of `( x + y)/( x - y), (x^2 - y^2)/(x^2y^2)`
Find the third proportion to the following :
(x - y) and m (x - y)
Determine if the following numbers are in proportion:
22, 33, 42, 63
In proportion, the 1st, 2nd, and 4th terms are 51, 68, and 108 respectively. Find the 3rd term.
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
The length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?
If b : a = c : d, then a, b, c, d are in proportion.
There is a number in the box `square` such that `square`, 24, 9, 12 are in proportion. The number in the box is ______.
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
39 litres : 65 litres and 6 bottles : 10 bottles
