Advertisements
Advertisements
Question
If (7a + 8b)(7c – 8d) = (7a – 8b)(7c + 8d); prove that a : b = c : d.
Solution
Given, `(7a + 8b)/(7a - 8b) = (7c + 8d)/(7c - 8d)` ...(Invertendo)
Applying componendo and dividendo,
`(7a + 8b + 7a - 8b)/(7a + 8b - 7a + 8b) = (7c + 8d + 7c - 8d)/(7c + 8d - 7c + 8d)`
`=> (14a)/(16b) = (14c)/(16d)`
`=> a/b = c/d`
Hence, a : b = c : d.
APPEARS IN
RELATED QUESTIONS
if `(x^2 + y^2)/(x^2 - y^2) = 17/8`then find the value of :
1) x : y
2) `(x^3 + y^3)/(x^3 - y^3)`
If a : b = c : d, prove that: (9a + 13b)(9c – 13d) = (9c + 13d)(9a – 13b).
If `x = (sqrt(m + n) + sqrt(m - n))/(sqrt(m + n) - sqrt(m - n))`, express n in terms of x and m.
If (7m +8n)(7p - 8q) = (7m - 8n)(7p + 8q), then prove that m: n = p: q
If a : b :: c : d :: e : f, then prove that `("ae" + "bf")/("ae" - "bf")` = `("ce" + "df")/("ce" - "df")`
Find x, if `16((a - x)/(a + x))^3 = (a + x)/(a - x)`.
Show, that a, b, c, d are in proportion if:
(6a + 7b) : (6c + 7d) : : (6a - 7b) : (6c - 7d)
If y = `(sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, show that 3by2 - 2ay + 3b = 0.
If `(3x + 4y)/(3u + 4v) = (3x - 4y)/(3u - 4v)`, then show that `x/y = u/v`.
If (m + n) : (n – m) = 5 : 2 ; m : n is ______.
