Advertisements
Advertisements
प्रश्न
If (7m +8n)(7p - 8q) = (7m - 8n)(7p + 8q), then prove that m: n = p: q
उत्तर
(7m +8n)(7p - 8q) = (7m - 8n)c
`=> (7"m" +8"n")/(7"m" - 8"n") = (7"p" + 8"q")/(7"p" - 8"q")`
Applying componendo and dividendo,
`(7"m" + 8"n" + 7"m" - 8"n")/(7"m" + 8"m" - 7"m" + 8"n") = (7"p" + 8"q" + 7"m" - 8"q")/(7"m" + 8"q" - 7"m" + 8"q")`
`=> (14 "m")/(16 "n") = (14"p")/(16"q")`
Dividing both sides by `14/16`
`"m"/"n" = "p"/"q"`
Hence. m:n = p : q .
APPEARS IN
संबंधित प्रश्न
Given `(x^3 + 12x)/(6x^2 + 8) = (y^3+ 27y)/(9y^2 + 27)`. Using componendo and dividendo find x : y.
If a : b = c : d, prove that: 5a + 7b : 5a – 7b = 5c + 7d : 5c – 7d.
If a : b :: c : d :: e : f, then prove that `("ae" + "bf")/("ae" - "bf")` = `("ce" + "df")/("ce" - "df")`
If `p/q = r/s`, prove that `(2p + 3q)/(2p - 3q) = (2r + 3s)/(2r - 3s)`.
If a : b : : c : d, prove that `(5a + 11b)/(5c + 11d) = (5a - 11b)/(5c - 11d)`
If a : b : : c : d, prove that (2a + 3b)(2c – 3d) = (2a – 3b)(2c + 3d)
Using the properties of proportion, solve the following equation for x; given `(x^3 + 3x)/(3x^2 + 1) = (341)/(91)`
If x = `(2mab)/(a + b)`, find the value of `(x + ma)/(x - ma) + (x + mb)/(x - mb)`
If x = `"pab"/(a + b)`, provee that `(x + pa)/(x - pa) - (x + pb)/(x - pb) = (2(a^2 - b^2))/(ab)`
If (m + n) : (n – m) = 5 : 2 ; m : n is ______.
