Advertisements
Advertisements
Question
If `x^2 + (1)/x^2 = 18`; find : `x^3 - (1)/x^3`
Sum
Advertisements
Solution
`(x^3 - (1)/x)^3`
= `x^3 - (1)/x^3 - 3(x - 1/x)`
⇒ 64 = `x^3 - (1)/x^3 - 3(4)`
⇒ `x^3 - (1)/x^3`
= 64 + 12
= 76.
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
Simplify.
(3r − 2k)3 + (3r + 2k)3
If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^3 - 1/a^3 )`
If X ≠ 0 and X + `1/"X"` = 2 ; then show that :
`x^2 + 1/x^2 = x^3 + 1/x^3 = x^4 + 1/x^4`
If `5x + (1)/(5x) = 7`; find the value of `125x^3 + (1)/(125x^3)`.
If `3x - (1)/(3x) = 9`; find the value of `27x^3 - (1)/(27x^3)`.
If `"a" - (1)/"a" = 7`, find `"a"^2 + (1)/"a"^2 , "a"^2 - (1)/"a"^2` and `"a"^3 - (1)/"a"^3`
If a + b = 5 and ab = 2, find a3 + b3.
Evaluate the following :
(5.45)3 + (3.55)3
Expand: `[x + 1/y]^3`
If `x^2 + 1/x^2` = 23, then find the value of `x + 1/x` and `x^3 + 1/x^3`
