Advertisements
Advertisements
Question
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)`
Solution
7x – 15y = 4x + y
7x – 4x = y + 15y
3x = 16y
`x/y = 16/3`
`=> x^2/y^2 = 256/9`
`=> (3x^2)/(2y^2) = (768)/18 = 128/3` ...`("Multiplying both sides by" 3/2)`
`=> (3x^2 + 2y^2)/(3x^2 - 2y^2) = (128 + 3)/(128 - 3)` ...(Applying componendo and dividendo)
`=> (3x^2 + 2y^2)/(3x^2 - 2y^2) = 131/125`
APPEARS IN
RELATED QUESTIONS
Given `(x^3 + 12x)/(6x^2 + 8) = (y^3+ 27y)/(9y^2 + 27)`. Using componendo and dividendo find x : y.
if `(x^2 + y^2)/(x^2 - y^2) = 17/8`then find the value of :
1) x : y
2) `(x^3 + y^3)/(x^3 - y^3)`
If (7m +8n)(7p - 8q) = (7m - 8n)(7p + 8q), then prove that m: n = p: q
If `a/b = c/d,` show that (9a + 13b) (9c - 13d) = (9c + 13b) (9a - 13d).
If `(3x + 4y)/(3u + 4v) = (3x - 4y)/(3u - 4v)`, then show that `x/y = u/v`.
If x = `(2a + b)/(a + b)` find the value of `(x + a)/(x - a) + (x + b)/(x - b)`
Solve `(1 + x + x^2)/(1 - x + x^2) = (62(1 +x))/(63(1 + x)`
If x = `(sqrt(a + 1) + sqrt(a - 1))/(sqrt(a + 1 - sqrt(a - 1)`, using properties of proportion, show that x2 – 2ax + 1 = 0
Using the properties of proportion, solve the following equation for x; given `(x^3 + 3x)/(3x^2 + 1) = (341)/(91)`
If (m + n) : (n – m) = 5 : 2 ; m : n is ______.
