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)`
Advertisements
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.
`4/(7+ 4 sqrt3)`
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
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)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
If x = `sqrt3 - sqrt2`, find the value of:
(i) `x + 1/x`
(ii) `x^2 + 1/x^2`
(iii) `x^3 + 1/x^3`
(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`
