Advertisements
Advertisements
Question
If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.
Advertisements
Solution
`(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)`
= `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) xx (sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) - sqrt(0.75))`
= `(sqrt(2.5) - sqrt(0.75))^2/((sqrt(2.5))^2 - (sqrt(0.75))^2`
= `(2.5 - 2 xx sqrt(2.5) xx sqrt(0.75) + 0.75)/(2.5 - 0.75)`
= `(3.25 - 2 xx sqrt(0.25 xx 10) xx sqrt(0.25 xx 3))/(1.75)`
= `(3.25 - 2 xx 0.25sqrt(30))/(1.75)`
= `(3.25 - 0.5sqrt(30))/(1.75)`
= `(3.25)/(1.75) - (0.5)/(1.75)sqrt(30)`
= `(325)/(175) - (50)/(175)sqrt(30)`
= `(13)/(7) - (2)/(7)sqrt(30)`
= `(13)/(7) + (-2/7)sqrt(30)`
= p + q`sqrt(30)`
Hence, p = `(13)/(7)` and q = `-(2)/(7)`.
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`1/sqrt5`
Rationalise the denominators of : `[ 2 - √3 ]/[ 2 + √3 ]`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
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 value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
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)`
