Advertisements
Advertisements
प्रश्न
If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d
Advertisements
उत्तर
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
(ma + nb) : b = (mc + nd) : d
⇒ `"ma + nb"/b = "mc + nd"/d`
L.H.S. = `"mbk + nb"/b`
= `(b("mk + n"))/b`
= mk + n
R.H.S. = `"mc + nd"/d`
= `"mdk + nd"/d`
= `(d("mk + n"))/d`
= mk + n.
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
If `a/b = c/d` prove that each of the given ratios is equal to
`(5a + 4c)/(5b + 4d)`
If q is the mean proportional between p and r prove that `(p^3 + q^3 + r^3)/(p^2q^2r^2) = 1/p^3 + 1/q^3 = 1/r^3`
Find the value of the unknown in the following proportion :
5 : 12 :: 15 : x
If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3)
`("pqr")^2 (1/"p"^4 + 1/"q"^4 + 1/"r"^4) = ("p"^4 + "q"^4 + "r"^4)/"q"^2`
If p, q and r in continued proportion, then prove the following :
`"p"^2 - "q"^2 + "r"^2 = "q"^4 (1/"p"^2 - 1/"q"^2 - 1/"r"^2)`
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
Find the missing number in the box in the proportion:
`square/18 = 2/9`
Write True (T) or False (F) against the following statement:
8 : 9 : : 24 : 27
What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?
Which of the following statements correctly defines a proportion involving four non-zero quantities a, b, c, and d?
