Advertisements
Advertisements
प्रश्न
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
Advertisements
उत्तर
x2 - y2 + xy
x2 - y2 + xy = (x + y) (x - y) + xy ----(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
(x - y) = `((sqrt(3) + 1))/((sqrt(3) - 1)) xx ((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)`
= `2sqrt(3)`
and xy = `((sqrt(3) + 1))/((sqrt(3) - 1)) xx ((sqrt(3) - 1))/((sqrt(3) + 1)`
= `(3 - 1)/(3 - 1)`
= 1
substitutingin (1), we get
x2 - y2 + xy
= (x+ y) (x - y) + xy
= `4 xx 2sqrt(3) + 1`
= `8sqrt(3) + 1`
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`1/(sqrt 3 - sqrt 2)`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
Simplify the following :
`sqrt(6)/(sqrt(2) + sqrt(3)) + (3sqrt(2))/(sqrt(6) + sqrt(3)) - (4sqrt(3))/(sqrt(6) + sqrt(2)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
In the following, find the values of a and b:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
In the following, find the values of a and b:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
