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 (7a + 8b)(7c – 8d) = (7a – 8b)(7c + 8d); prove that a : b = c : d.
If `(x^3 + 3xy^2)/(3x^2y + y^3) = (m^3 + 3mn^2)/(3m^2n + n^3)`, show that nx = my.
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)`
Given that `(a^3 + 3ab^2)/(b^2 + 3a^2b) = (63)/(62)`.
Using Componendo and Dividendo find a : b.
If (4a + 5b) (4c – 5d) = (4a – 5d) (4c + 5d), prove that a, b, c, d are in proporton.
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 x = `(root(3)(a + 1) + root(3)(a - 1))/(root(3)(a + 1) - root(3)(a - 1)`,prove that :
x³ – 3ax² + 3x – a = 0
Using Componendo and Dividendo solve for x:
`(sqrt(2x + 2) + sqrt(2x - 1))/(sqrt(2x + 2) - sqrt(2x - 1))` = 3
If (a + b) : (a – b) = 13 : 3 ; a : b is ______.
