Advertisements
Advertisements
प्रश्न
If (7a + 8b)(7c – 8d) = (7a – 8b)(7c + 8d); prove that a : b = c : d.
उत्तर
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
संबंधित प्रश्न
If a : b = c : d, prove that: xa + yb : xc + yd = b : d.
If `x = (6ab)/(a + b)`, find the value of `(x + 3a)/(x - 3a) + (x + 3b)/(x - 3b)`.
If 7x – 15y = 4x + y, find the value of x : y. Hence, use componendo and dividend to find the values of:
`(3x^2 + 2y^2)/(3x^2 - 2y^2)`
If `(x^2 + y^2)/(x^2 - y^2) = 2 1/8`, find: `(x^3 + y^3)/(x^3 - y^3)`
If a : b = c : d , then prove that `("a"^2 + "ab" +
"b"^2)/("a"^2 - "ab" + "b"^2) = ("c"^2 + "cd"+ "d"^2)/("c"^2 - "cd" + "d"^2)`
if `(3a + 4b)/(3c + 4d) = (3a - 4b)/(3c - 4d)` Prove that `a/b = c/d`.
Find x from the following equations : `(sqrt(1 + x) + sqrt(1 - x))/(sqrt(1 + x) - sqrt(1 - x)) = a/b`
Find x from the following equations : `(sqrt(12x + 1) + sqrt(2x - 3))/(sqrt(12x + 1) - sqrt(2x - 3)) = (3)/(2)`
Solve for `x : 16((a - x)/(a + x))^3 = (a + x)/(a - x)`
If `(x^2 - 1)/(x^2 + 1) = 3/5`, the value of x is ______.
