Advertisements
Advertisements
प्रश्न
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
Advertisements
उत्तर
`sqrt(x) + (1)/(sqrt(x)`
Squaring Both sides we get
`(sqrt(x) + (1)/sqrt(x))^2 = x + (1)/x + 2` ----(1)
We will first find out `x + (1)/x`
`x + (1)/x = (7 + 4sqrt(3)) + (1)/((7 + 4sqrt(3))`
= `((7 + 4sqrt(3)^2 + 1))/((7 + 4sqrt(3))`
= `(49 + 48 + 56sqrt(3) + 1)/((7 + 4sqrt(3))`
= `(98 + 56sqrt(3))/((7 + 4sqrt(3))`
= `(14(7 + 4sqrt(3)))/((7 + 4sqrt(3))`
= 14
substitutingin (1)
`(sqrt(x) + (1)/sqrt(x))^2 = x + (1)/x + 2`
= 14 + 2
= 16
∴ `sqrt(x) + (1)/sqrt(x)` = 4
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Rationalise the denominator of `1/[ √3 - √2 + 1]`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
Simplify by rationalising the denominator in the following.
`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x2 + y2
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
Using the following figure, show that BD = `sqrtx`.
