Advertisements
Advertisements
Question
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
Advertisements
Solution
`(1)/(sqrt(5) - sqrt(3)`
= `(1)/(sqrt(5) - sqrt(3)) xx (sqrt(5) + sqrt(3))/(sqrt(5) + sqrt(3)`
= `(sqrt(5) + sqrt(3))/((sqrt(5))^2 - (sqrt(3))^2`
= `(sqrt(5) + sqrt(3))/(5 - 3)`
= `(sqrt(5) + sqrt(3))/(2)`
= `(1)/(2)sqrt(5) + (1)/(2)sqrt(3)`
= `(1)/(2)sqrt(5) - (-1/2)sqrt(3)`
= `"a"sqrt(5) - "b"sqrt(3)`
Hence, a = `(1)/(2)` and b = `-(1)/(2)`.
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Rationalize the denominator.
`1/(sqrt 3 - sqrt 2)`
Simplify : `sqrt18/[ 5sqrt18 + 3sqrt72 - 2sqrt162]`
Simplify by rationalising the denominator in the following.
`(sqrt(5) - sqrt(7))/sqrt(3)`
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(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 = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x3 + y3
Draw a line segment of length `sqrt3` cm.
Using the following figure, show that BD = `sqrtx`.
