Advertisements
Advertisements
प्रश्न
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x3 + y3
Advertisements
उत्तर
x3 + y3
x3 + y3 = (x + y)3 - 3xy(x + y) ----(1)
∴ (x + y) = `((sqrt(3) + 1))/((sqrt(3) - 1)) + ((sqrt(3) - 1))/((sqrt(3) + 1)`
= `((sqrt(3) + 1)^2 + (sqrt(3) - 1)^2)/(3 - 1)`
= `(3 + 1 + 2sqrt(3) + 3 + 1 - 2sqrt(3))/(2)`
= `(8)/(2)`
= 4
and xy = `((sqrt(3) + 1))/((sqrt(3) - 1)) xx ((sqrt(3) - 1))/((sqrt(3) + 1)`
= `(3 - 1)/(3 - 1)`
= 1
substitutingin (1), we get
x3 + y3
= (x + y)3 - 3xy(x + y)
= 64 - 3 x 4
= 64 - 12
= 52
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`2/(3 sqrt 7)`
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
Simplify by rationalising the denominator in the following.
`(3sqrt(2))/sqrt(5)`
Simplify by rationalising the denominator in the following.
`(sqrt(5) - sqrt(7))/sqrt(3)`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
