Advertisements
Advertisements
Question
If `9"a"^2 + (1)/(9"a"^2) = 23`; find the value of `27"a"^3 + (1)/(27"a"^3)`
Advertisements
Solution
`9"a"^2 + (1)/(9"a"^2) = 23`
Using `(3"a" + 1/(3"a"))^2`
= `(3"a")^2 + (1/(3"a"))^2 + 2(3"a") (1/(3"a"))`
⇒ `(3"a" + 1/(3"a"))^2`
= `9"a"^2 + 1/(9"a"^2) + 2`
= 23 + 2
= 25
⇒ `3"a" + 1/(3"a")` = 5
Cubing both sides, we get :
`(3"a")^3 + (1/(3"a"))^3 + 3(3"a") (1/(3"a")) (3"a" + 1/(3"a"))` = (5)3
⇒ `27"a"^3 + 1/(27"a"^3) + 3(5)` = 125
⇒ `27"a"^3 + 1/(27"a"^3)`
= 125 - 15
= 110.
APPEARS IN
RELATED QUESTIONS
If `a^2 + 1/a^2` = 18; a ≠ 0 find :
(i) `a - 1/a`
(ii) `a^3 - 1/a^3`
If `a + 1/a` = p and a ≠ 0; then show that:
`a^3 + 1/a^3 = p(p^2 - 3)`
If `5x + (1)/(5x) = 7`; find the value of `125x^3 + (1)/(125x^3)`.
If `"a" - (1)/"a" = 7`, find `"a"^2 + (1)/"a"^2 , "a"^2 - (1)/"a"^2` and `"a"^3 - (1)/"a"^3`
If `x^2 + (1)/x^2 = 18`; find : `x^3 - (1)/x^3`
If `"a" + (1)/"a" = "p"`; then show that `"a"^3 + (1)/"a"^3 = "p"("p"^2 - 3)`
If 2a - 3b = 10 and ab = 16; find the value of 8a3 - 27b3.
Expand: (3x + 4y)3.
If `"a" + 1/"a"` = 6, then find the value of `"a"^3 + 1/"a"^3`
Expand (104)3
