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
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/sqrt5`
Rationalise the denominators of : `3/sqrt5`
Rationalise the denominators of : `3/[ sqrt5 + sqrt2 ]`
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
Rationalise the denominator of `1/[ √3 - √2 + 1]`
If `sqrt2` = 1.4 and `sqrt3` = 1.7, find the value of `(2 - sqrt3)/(sqrt3).`
Simplify by rationalising the denominator in the following.
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
Show that: `(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
