Advertisements
Advertisements
प्रश्न
If a, b, c, d are in continued proportion, prove that: `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3) = a/d`
Advertisements
उत्तर
a, b, c, d are in continued proportion
∴ `a/b = b/c = c/d` = k(say)
∴ c = dk, b = ck = dk2, a = bk = dk3
L.H.S.
= `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3)`
= `((dk^3)^3 + (dk^2)^3 + (dk)^3)/((dk^2)^3 + (dk)^3 + d^3)`
= `(d^3k^9 + d^3k^6 + d^3k^3)/(d^3k^6 + d^3k^3 + d^3)`
= `(d^3k^3(k^6 + k^3 + 1))/(d^3(k^6 + k^3 + 1)`
= k3
R.H.S.
= `a/d`
= `(dk^3)/d`
= k3
∴ L.H.S. = R.H.S.
संबंधित प्रश्न
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find m : n
Find the smallest number that must be subtracted from each of the numbers 20, 29, 84 and 129 so that they are in proportion.
What least number must be added to each of the numbers 5, 11, 19 and 37, so that they are in proportion?
Determine if the following ratio form a proportion:
2 kg : 80 kg and 25 g : 625 kg
The weight of 65 books is 13 kg.
(i) What is the weight of 80 such books?
(ii) How many such books weigh 6.4 kg?
In an army camp, there were provisions for 550 men for 28 days. But, 700 men attended the camp. How long did the provisions last?
The angles of a triangle are in the ratio 3 : 1 : 2. The measure of the largest angle is
If a, b, c are in continued proportion, prove that: `(pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c`
Unequal masses will not balance on a fulcrum if they are at equal distance from it; one side will go up and the other side will go down.
Unequal masses will balance when the following proportion is true:
`("mass"1)/("length"2) = ("mass"2)/("length"1)`
Two children can be balanced on a seesaw when
`("mass"1)/("length"2) = ("mass"2)/("length"1)`. The child on the left and child on the right are balanced. What is the mass of the child on the right?
