Advertisements
Advertisements
प्रश्न
If a ≠ 0 and `a- 1/a` = 3 ; Find :
`a^3 - 1/a^3`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Expand.
(7 + m)3
Expand.
(52)3
Use property to evaluate : 383 + (-26)3 + (-12)3
Find the cube of: `(2"m")/(3"n") + (3"n")/(2"m")`
If `"p" + (1)/"p" = 6`; find : `"p"^3 + (1)/"p"^3`
If `"a" + (1)/"a" = "p"`; then show that `"a"^3 + (1)/"a"^3 = "p"("p"^2 - 3)`
If `("a" + 1/"a")^2 = 3`; then show that `"a"^3 + (1)/"a"^3 = 0`
If a + b = 5 and ab = 2, find a3 + b3.
Simplify:
(a + b)3 + (a - b)3
If `x^2 + 1/x^2` = 23, then find the value of `x + 1/x` and `x^3 + 1/x^3`
