Advertisements
Advertisements
Question
If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3)
Advertisements
Solution
`"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
RELATED QUESTIONS
If p, q and r in continued proportion, then prove the following:
(p + q + r )(p - q + r) = p2 + q2 + r2
If a, b, c and dare in continued proportion, then prove that
(a+ d)(b+ c)-(a+ c)(b+ d)= (b-c)2
If a, b, c are in continued proportion and a(b – c) = 2b, prove that: `a - c = (2(a + b))/a`.
If `a/b = c/d = r/f`, prove that `((a^2b^2 + c^2d^2 + e^2f^2)/(ab^3 + cd^3 + ef^3))^(3/2) = sqrt((ace)/(bdf)`
If b is the mean proportional between a and c, prove that a, c, a² + b², and b² + c² are proportional.
3 : 5 : : `square` : 20
Which of the following ratios are in proportion?
Determine if the following are in proportion.
15, 45, 40, 120
A student said that the ratios `3/4` and `9/16` were proportional. What error did the student make?
If `(a + b)^3/(a - b)^3 = 64/27`
- Find `(a + b)/(a - b)`
- Hence using properties of proportion, find a : b.
