Advertisements
Advertisements
प्रश्न
If (ma + nb): b :: (mc + nd) : d, prove that a, b, c, d are in proportion.
उत्तर
(ma + nb): b :: (mc + nd) : d
⇒ `"ma + nb"/"b" = "mc + nd"/"d"`
⇒ mad + nbd = mbc + nbd
⇒ mad = mbc
⇒ ad = bc
⇒ `a/b = c/d`
Hence a : b :: c : d
APPEARS IN
संबंधित प्रश्न
if x = `(sqrt(a + 1) + sqrt(a-1))/(sqrt(a + 1) - sqrt(a - 1))` using properties of proportion show that `x^2 - 2ax + 1 = 0`
If `x = (6ab)/(a + b)`, find the value of `(x + 3a)/(x - 3a) + (x + 3b)/(x - 3b)`.
Given that `(a^3 + 3ab^2)/(b^2 + 3a^2b) = (63)/(62)`.
Using Componendo and Dividendo find a : b.
Given : x = `(sqrt(a^2 + b^2)+sqrt(a^2 - b^2))/(sqrt(a^2 + b^2)-sqrt(a^2 - b^2))`
Use componendo and dividendo to prove that `b^2 = (2a^2x)/(x^2 + 1)`.
If (a + 3b + 2c + 6d) (a – 3b – 2c + 6d) = (a + 3b – 2c – 6d) (a – 3b + 2c – 6d), prove that a : b :: c : d.
If x = `(8ab)/"a + b"` find the value of `(x + 4a)/(x - 4a) + (x + 4b)/(x - 4b)`
Find x from the following equations : `(sqrt(2 - x) + sqrt(2 + x))/(sqrt(2 - x) - sqrt(2 + x)` = 3
If (3x² + 2y²) : (3x² – 2y²) = 11 : 9, find the value of `(3x^4 + 5y^4)/(3x^4 - 5y^4)`
If a : b = 2 : 1, the value of (7a + 4b) : (5a – 2b) is ______.
If x = y, the value of (3x + y) : (5x – 3y) is ______.
