Advertisements
Advertisements
Question
If a ≠ 0 and `a- 1/a` = 3 ; Find :
`a^3 - 1/a^3`
Sum
Advertisements
Solution
`a- 1/a` = 3...............(Given)
Taking a cube on both sides,
`( a - 1/a )^3 = 3^3`
`a^3 - 1/a^3 - 3( a - 1/a) = 27`..............[(a - b)3 = a3 - b3 -3ab(a - b)]
`a^3 - 1/a^3 - 3 × 3 = 27..............[a- 1/a = 3]`
`a^3 - 1/a^3 - 9 = 27`
`a^3 - 1/a^3` = 27 + 9
`a^3 - 1/a^3` = 36.
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
If a2 + `1/a^2 = 47` and a ≠ 0 find :
- `a + 1/a`
- `a^3 + 1/a^3`
If a ≠ 0 and `a - 1/a` = 3 ; find `a^2 + 1/a^2`
Find the cube of: 4x + 7y
Find the cube of: `4"p" - (1)/"p"`
If `"p" + (1)/"p" = 6`; find : `"p"^3 + (1)/"p"^3`
If a + b = 5 and ab = 2, find a3 + b3.
If m - n = -2 and m3 - n3 = -26, find mn.
Expand: (41)3
Expand: `((2m)/n + n/(2m))^3`.
a3 + b3 = (a + b)3 = __________
