Advertisements
Advertisements
प्रश्न
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
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.
`1/(3 sqrt 5 + 2 sqrt 2)`
Rationalise the denominators of : `[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Simplify by rationalising the denominator in the following.
`(42)/(2sqrt(3) + 3sqrt(2)`
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
If x = `(7 + 4sqrt(3))`, find the values of
`x^3 + (1)/x^3`
Draw a line segment of length `sqrt5` cm.
Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
