Advertisements
Advertisements
प्रश्न
If `a/c = c/d = c/f` prove that : `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3` = 27(a + b)(c + d)(e + f)
Advertisements
उत्तर
`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e =fk
L.H.S. = `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3`
= `bd f[(bk + b)/b + (dk + d)/d + (fk + f)/f]^3`
= `bd f[(b(k + 1))/b + (d(k + 1))/d + (f(k + 1))/f]^3`
= bdf(k + 1 + k + 1 + k + 1)3
= bdf(3k + 3)3 = 27bdf(k + 1)3
R.H.S. = 27(a + b)(c + d)(e + f)
= 27(bk + b)(dk + d)(fk + f)
= 27b(k + 1)d(k + 1)f(k + 1)
= 27bdf(k + 1)3
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the mean proportional between a – b and a3 – a2b
If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
An electric pole casts a shadow of length 20 m at a time when a tree 6 m high casts a shadow of length 8 m. Find the height of the pole.
If the cost of a dozen soaps is Rs 285.60, what will be the cost of 15 such soaps?
4.5 g of an alloy of copper and zinc contains 3.5 g of copper. What weight of copper will there be in 18.9 g of the alloy?
The cost of 18 chairs is Rs 22770. How many such chairs can be bought for Rs 10120?
Choose the correct answer from the given options :
The third proportional to `6(1)/(4)` and 5 is
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion?
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
200 mL : 2.5 litre and ₹ 4 : ₹ 50
