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.
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 : `[ 2 - √3 ]/[ 2 + √3 ]`
Rationalise the denominators of : `3/[ sqrt5 + sqrt2 ]`
Rationalise the denominators of : `[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
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 value of a and b:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
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`
Draw a line segment of length `sqrt8` cm.
