Advertisements
Advertisements
प्रश्न
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
पर्याय
5
4
3
2
उत्तर
In the given problem, we have to find the value of `x-1/x`
Given `x^3 - 1/x^3 = 14`
We shall use the identity `(a-b)^3 = a^3 -b^3-3ab (a-b)`
`(x-1/x)^3 = x^3 - 1/x^3 - 3 xx x xx 1/x(x-1/x)`
`(x = 1/x)^3 = x^3 - 1/x^3 -3 (x-1/x)`
Put `x- 1/x = y` we get,
`(y)^3 = x^3 -1/x^3 -3(y)`
Substitute y = 2 in above equation we get,
`(2)^3 = x^3 -1/x^3 - 3 (2) `
`8 = x^3 - 1/x^3 -6`
`8+6 = x^2 -1/x^3`
`14 = x^3 - 1/x^3`
The Equation `(y )^3 = x^3 - 1/x^3 -3(y)`satisfy the condition that `x^3 - 1/x^3 = 14`
Hence the value of `x - 1 /x`is 2
APPEARS IN
संबंधित प्रश्न
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Simplify of the following:
(x+3)3 + (x−3)3
Simplify of the following:
(2x − 5y)3 − (2x + 5y)3
Find the following product:
Find the square of : 3a - 4b
Use identities to evaluate : (101)2
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
Use direct method to evaluate the following products :
(x + 8)(x + 3)
Use the direct method to evaluate the following products :
(5a + 16) (3a – 7)
Use the direct method to evaluate :
(2+a) (2−a)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Find the squares of the following:
(2a + 3b - 4c)
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
