Advertisements
Advertisements
Question
If `("a" + 1/"a")^2 = 3`; then show that `"a"^3 + (1)/"a"^3 = 0`
Sum
Advertisements
Solution
`("a" + 1/"a")^2 = 3`
⇒ `"a" + (1)/"a" = sqrt(3)`
Now, `("a" + 1/"a")^3`
= `"a"^3 + (1)/"a"^3 + 3("a" + 1/"a")`
⇒ `(sqrt(3))^3`
= `"a"^3 + (1)/"a"^3 + 3(sqrt(3))`
⇒ `"a"^3 + (1)/"a"^3`
= `3sqrt(3) - 3sqrt(3)`
= 0.
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
Expand.
(101)3
Expand.
`(x + 1/x)^3`
If a ≠ 0 and `a - 1/a` = 3 ; find `a^2 + 1/a^2`
Find the cube of: `4"p" - (1)/"p"`
Find the cube of: `(2"m")/(3"n") + (3"n")/(2"m")`
If `3x - (1)/(3x) = 9`; find the value of `27x^3 - (1)/(27x^3)`.
If `x + (1)/x = 5`, find the value of `x^2 + (1)/x^2, x^3 + (1)/x^3` and `x^4 + (1)/x^4`.
Expand (3 + m)3
Expand (2a + 5)3
Find the volume of the cube whose side is (x + 1) cm
