Advertisements
Advertisements
प्रश्न
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
Advertisements
उत्तर
`x^2 + (1)/x^2`
`(x^2 + (1)/x^2) = (x + (1)/x)^2 - 2` ----(1)
We 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)
`(x^2 + (1)/x)^2 = (x + (1)/x)^2 -2`
= 196 - 2
= 194
∴ `(x^2 + (1)/x^2)` = 194
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Rationalise the denominators of : `3/[ sqrt5 + sqrt2 ]`
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
Simplify the following :
`sqrt(6)/(sqrt(2) + sqrt(3)) + (3sqrt(2))/(sqrt(6) + sqrt(3)) - (4sqrt(3))/(sqrt(6) + sqrt(2)`
In the following, find the values of a and b:
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
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 = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
Draw a line segment of length `sqrt3` cm.
