Advertisements
Advertisements
Question
If a ≠ 0 and `a- 1/a` = 3 ; Find :
`a^3 - 1/a^3`
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.
APPEARS IN
RELATED QUESTIONS
Expand.
(101)3
Find the cube of: `( 3a - 1/a ) (a ≠ 0 )`
If `a + 1/a` = p and a ≠ 0; then show that:
`a^3 + 1/a^3 = p(p^2 - 3)`
If `( a + 1/a )^2 = 3 "and a ≠ 0; then show:" a^3 + 1/a^3 = 0`.
Use property to evaluate : 73 + 33 + (-10)3
Find the cube of: 4x + 7y
If `"a" + (1)/"a" = "p"`; then show that `"a"^3 + (1)/"a"^3 = "p"("p"^2 - 3)`
If x3 + y3 = 9 and x + y = 3, find xy.
Expand (52)3
Find the volume of the cube whose side is (x + 1) cm
