Advertisements
Advertisements
प्रश्न
If `(8a - 5b)/(8c - 5a) = (8a + 5b)/(8c + 5d)`, prove that `a/b = c/d`
उत्तर
`(8a - 5b)/(8c - 5a) = (8a + 5b)/(8c + 5d)`
⇒ `(8a + 5b)/(8a - 5b) = (8c + 5b)/(8c - 5d)` ...(using alternendo)
Applying componendo and dividendo,
`(8a + 5b + 8a - 5b)/(8a + 5b - 8a + 5b) = (8c + 5d + 8c - 5c)/(8c + 5d - 8c + 5d)`
∴ `(16a)/(10b) = (16c)/(10d)`
⇒ `a/b = c/d ...("Dividing by" 16/10)`
Hence proved.
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 a : b = c : d, prove that: xa + yb : xc + yd = b : d.
If a : b = c : d, prove that: (6a + 7b)(3c – 4d) = (6c + 7d)(3a – 4b).
If `(a - 2b - 3c + 4d)/(a + 2b - 3c - 4d) = (a - 2b + 3c - 4d)/(a + 2b + 3c + 4d)`, show that: 2ad = 3bc.
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 `x = (sqrt(a + 1) + sqrt(a - 1))/(sqrt(a + 1) - sqrt(a - 1))`, using properties of proportion show that: x2 – 2ax + 1 = 0.
If `(7"a" + 12"b")/(7"c" + 12"d")` then prove that `"a"/"b"="c"/"d"`
Show, that a, b, c, d are in proportion if:
(6a + 7b) : (6c + 7d) : : (6a - 7b) : (6c - 7d)
If y = `((p + 1)^(1/3) + (p - 1)^(1/3))/((p + 1)^(1/3) - (p - 1)^(1/3)` find that y3 - 3py2 + 3y - p = 0.
Solve x : `(sqrt(36x + 1) + 6sqrt(x))/(sqrt(36x + 1) -6sqrt(x))` = 9
