Advertisements
Advertisements
प्रश्न
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
Advertisements
उत्तर
`x^3 + (1)/x^3`
`(x^3 + (1)/x^3) = (x + (1)/x)^3 -3(x + (1)/x)` -----(1)
we will first find the value of `x + (1)/x`
`x + (1)/x = (4 - sqrt(15)) + (1)/((4 - sqrt(15))`
= `((4 - sqrt(15))^2 + 1)/((4 - sqrt(15))`
= `(16 + 15 - 8sqrt(15) + 1)/((4 - sqrt(15))`
= `(8(4 - sqrt(15)))/((4 - sqrt(15))`
= 8
substituting the valuesin (1)
`(x^3 + (1)/x^3) = (x + (1)/x)^3 -3(x + (1)/x)`
= 83 - 24
= 488
`(x^3 + (1)/x^3)` = 488
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`1/sqrt5`
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Rationalise the denominators of : `[ 2 - √3 ]/[ 2 + √3 ]`
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
In the following, find the values of a and b:
`(sqrt(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Draw a line segment of length `sqrt8` cm.
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
