Advertisements
Advertisements
प्रश्न
If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3)
Advertisements
उत्तर
`"u"/"v" = "v"/"w" = "w"/"x" = "a"`
w = ax
v = aw = a2x
u = av = a3x
LHS
`(2"u" + 3"x")/(3"u" + 4"x")`
`= (2"a"^3"x" + 3"x")/(3"a"^3"x" + 4"x")`
`= (2"a"^3 + 3)/(3"a"^3 + 4)`
RHS
`(2"u"^3 + 3"v"^3)/(3"u"^3 + 4"v"^3)`
`= (2"a"^9"x"^3 + 3"a"^6"x"^3)/(3"a"^9"x"^3 + 4"a"^6"x"^3)`
`= (2"a"^3 + 3)/(3"a"^3 + 4)`
LHS = RHS. Hence , proved.
APPEARS IN
संबंधित प्रश्न
What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
Given four quantities a, b, c and d are in proportion. Show that: (a – c)b2 : (b – d)cd = (a2 – b2 – ab) : (c2 – d2 – cd)
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
If q is the mean proportional between p and r, prove that
`p^2 - q^2 + r^2 = q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`.
Verify the following:
60 : 105 : : 84 : 147
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
If `a/c = c/d = c/f` prove that : `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"`
If a, b, c and d are in proportion, prove that: (5a + 7b) (2c – 3d) = (5c + 7d) (2a – 3b).
Find two numbers whose mean proportional is 16 and the third proportional is 128.
Find whether 12, 24, 18, 36 are in order that can be expressed as two ratios that are in proportion
