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
Rationalise the denominators of : `3/sqrt5`
Rationalise the denominators of : `1/(sqrt3 - sqrt2 )`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
Simplify the following
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
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 `sqrt5` cm.
Draw a line segment of length `sqrt8` cm.
