Advertisements
Advertisements
प्रश्न
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
उत्तर
`(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
संबंधित प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
Simplify by rationalising the denominator in the following.
`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`
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:
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
Draw a line segment of length `sqrt5` cm.
