Advertisements
Advertisements
प्रश्न
If `a/b = c/d = e/f`, prove that each ratio is `[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`
Advertisements
उत्तर
`a/b = c/d = e/f` = k(say)
∴ a = k, c = dk, e = fk
`[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`
= `[(2b^3k^3 + 5d^3k^3 + 7f^3k^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`
= `k[(2b^3 + 5d^3 + 7f^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)` = k
Hence proved.
APPEARS IN
संबंधित प्रश्न
If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b
By increasing the cost of entry ticket to a fair in the ratio 10 : 13, the number of visitors to the fair has decreased in the ratio 6 : 5. In what ratio has the total collection increased or decreased?
Find the duplicate ratio of the following :
(a+b): (a2- b2)
Express the following ratios in its simplest form :
5 kg: 800 gm
Express the following ratios in its simplest form :
2.5 : 1.5
Find the mean proportional between 0.9 and 2.5
How will Rs 31500 be shared between A, B, and C; if A gets the double of what B gets, and B gets the double of what C gets?
If (x + 2y) : (2x – y) is equal to the duplicate ratio of 3 : 2, find x : y.
An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 30 minutes. What is the ratio of lunch break to the total period in the office?
At the parking stand of Ramleela ground, Kartik counted that there are 115 cycles, 75 scooters and 45 bikes. Find the ratio of the number of cycles to the total number of vehicles.
