Advertisements
Advertisements
Question
If `(x^2 + y^2)/(x^2 - y^2) = 2 1/8`, find: `(x^3 + y^3)/(x^3 - y^3)`
Solution
`(x^3 + y^3)/(x^3 - y^3)`
= `((x/y)^3 + 1)/((x/y)^3 - 1)`
= `((5/3)^3 + 1)/((5/3)^3 - 1 )`
= `(125/27 + 1)/(125/27 - 1)`
= `((125 + 27)/27)/((125 - 27)/27)`
= `(125 + 27)/(125 - 27)`
= `76/49`
= `1 27/49`
APPEARS IN
RELATED QUESTIONS
Given `(x^3 + 12x)/(6x^2 + 8) = (y^3+ 27y)/(9y^2 + 27)`. Using componendo and dividendo find x : y.
Given `(x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27)` using componendo and divendo find x : y
If a : b =c : d, then prove that `("a"^2 + "c"^2)/("b"^2 + "d"^2) = ("ac")/("bc")`
Show, that a, b, c, d are in proportion if:
(6a + 7b) : (6c + 7d) : : (6a - 7b) : (6c - 7d)
If y = `(sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, show that 3by2 - 2ay + 3b = 0.
Find x from the following equations : `(sqrt(1 + x) + sqrt(1 - x))/(sqrt(1 + x) - sqrt(1 - x)) = a/b`
Using the properties of proportion, solve the following equation for x; given `(x^3 + 3x)/(3x^2 + 1) = (341)/(91)`
Using Componendo and Dividendo solve for x:
`(sqrt(2x + 2) + sqrt(2x - 1))/(sqrt(2x + 2) - sqrt(2x - 1))` = 3
If `(x^2 - 1)/(x^2 + 1) = 3/5`, the value of x is ______.
If (m + n) : (n – m) = 5 : 2 ; m : n is ______.
