Advertisements
Advertisements
प्रश्न
In the following, find the values of a and b:
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`
उत्तर
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)`
= `(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) xx (4sqrt(3) - 3sqrt(2))/(4sqrt(3) - 3sqrt(2)`
= `(7sqrt(3)(4sqrt(3) - 3sqrt(2)) - 5sqrt(2)(4sqrt(3) - 3sqrt(2)))/((4sqrt(3))^2 - (3sqrt(2))^2`
= `(84 - 21sqrt(6) - 20sqrt(6) + 30)/(48 - 18)`
= `(110 - 41sqrt(6))/(30)`
= `(110)/(30) - (41sqrt(6))/(30)`
= `(11)/(3) - (41)/(30)sqrt(6)`
= `"a" - "b"sqrt(6)`
Hence, a = `(11)/(3)` and b = `(41)/(30)`.
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
Rationalize the denominator.
`1/sqrt5`
If `sqrt2` = 1.4 and `sqrt3` = 1.7, find the value of `(2 - sqrt3)/(sqrt3).`
Simplify by rationalising the denominator in the following.
`(sqrt(5) - sqrt(7))/sqrt(3)`
Simplify the following
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
If x = `(7 + 4sqrt(3))`, find the values of
`x^3 + (1)/x^3`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
