Advertisements
Advertisements
प्रश्न
Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
Advertisements
उत्तर
Given: x = 2 + `sqrt3`
`1/x = 1/(2 + sqrt3) xx (2 - sqrt3)/(2 - sqrt3)`
`= (2 - sqrt3)/((2)^2 - (sqrt3)^2)`
`= (2 - sqrt3)/(4 - 3)`
`= 2 - sqrt3`
Now,
`x + 1/x = 2 + cancel(sqrt3) + 2 - cancel(sqrt3)`
`x + 1/x = 2 + 2`
`x + 1/x`= 4
`therefore x^3 + 1/x^3`
`= (x + 1/x)^3 - 3 * cancel(x) * 1/cancel(x) (x + 1/x)`
`= (4)^3 - 3 xx 4`
= 64 - 12
= 52
APPEARS IN
संबंधित प्रश्न
Simplify : `sqrt18/[ 5sqrt18 + 3sqrt72 - 2sqrt162]`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
In the following, find the value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
Draw a line segment of length `sqrt3` cm.
Show that: `x^2 + 1/x^2 = 34,` if x = 3 + `2sqrt2`
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
