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
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
Find the value of the unknown in the following proportion :
3 : 4 : : p : 12
Find the third proportion to the following :
`9/25` and `18/25`
If `a/b = c/d` Show that a + b : c + d = `sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`.
If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^2/b^2 + z^3/c^2 = ((x + y + z)^3)/((a + b ++ c)^2)`.
Verify the following:
108 : 72 : : 129 : 86
Determine if the following ratio form a proportion:
2 kg : 80 kg and 25 g : 625 kg
In covering 111 km, a car consumes 6 L of petrol. How many kilometers will it go to 10 L of petrol?
Which of the following ratios are in proportion?
Are the following statements true?
45 km : 60 km = 12 hours : 15 hours
