Advertisements
Advertisements
प्रश्न
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
Advertisements
उत्तर
x3 + y3
(x3 + y3) = (x + y)3 - 3xy (x + y) ----(1)
Now, x + y = `(1)/((3 - 2sqrt(2))) + (1)/((3 + 2sqrt(2))`
= `((3 + 2sqrt(2)) + (3 - 2sqrt(2)))/((3 - 2sqrt(2))(3 + 2sqrt(2))`
= `(6)/(9 - 8)`
= 6
and xy = `(1)/((3 - 2sqrt(2))) xx (1)/((3 + 2sqrt(2))`
= `(1)/(9 - 8)`
= 1
substituting the valuesin (1), we get
(x3 + y3)
= (x + y)3 - 3xy (x + y)
= 216 - 3 x 6
= 198
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
Rationalize the denominator.
`1/sqrt5`
Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`
Simplify by rationalising the denominator in the following.
`(3sqrt(2))/sqrt(5)`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
In the following, find the value of a and b:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`
In the following, find the value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "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 = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x3 + y3
