Advertisements
Advertisements
प्रश्न
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
Advertisements
उत्तर
Given that, `x= 2+sqrt3` hence
\[\frac{1}{x}\] is given as
. `1/x = 1/(2+sqrt3)`We are asked to find `x +1/x `
We know that rationalization factor for `2+sqrt3` is`2-sqrt3` . We will multiply each side of the given expression `1/(2+sqrt3)` by, `2-sqrt3` to get
. `1/x = 1/(2+sqrt3) xx(2-sqrt3)/(2-sqrt3)`
`= (2-sqrt3)/((2)^2-(sqrt3)^2)`
`= (2-sqrt3)/(4-3)`
`=2-sqrt3`
Therefore,
`x+1/x = 2+sqrt3 +2 - sqrt3`
`=4`
Hence value of the given expression is 4 .
APPEARS IN
संबंधित प्रश्न
Rationalise the denominator of the following
`sqrt2/sqrt5`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt2 - 1)/sqrt5`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`
if `x = 2 + sqrt3`,find the value of `x^2 + 1/x^2`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
