Advertisements
Advertisements
प्रश्न
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
Advertisements
उत्तर
In the given problem, we have to find the value of `x^3 - 1/x^3`
Given: `x - 1/x = 7`
We shall use the identity (a – b)3 = a3 – b3 – 3ab(a – b)
Here putting, `x - 1/x = 7`,
`(x - 1/x)^3 = x^3 - 1/x^3 - 3 (x xx 1/x)(x - 1/x)`
`(7)^3 = x^3 - 1/x^3 - 3 (x xx 1/x ) (x-1/x)`
`343 = x^3 - 1/x^3 - 3 (x - 1/x)`
`343 = x^3 - 1/x^3 - 3 xx 7 `
`343 = x^3 - 1/x^3 - 21`
`343 + 21 = x^3 - 1/x^3`
`343 = x^3 - 1/x^3`
Hence the value of `x^3 - 1/x^3` is 364.
APPEARS IN
संबंधित प्रश्न
Use suitable identity to find the following product:
(3 – 2x) (3 + 2x)
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
Simplify the following product:
(x2 + x − 2)(x2 − x + 2)
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
Use the direct method to evaluate :
(x+1) (x−1)
Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`
Find the squares of the following:
3p - 4q2
Find the squares of the following:
(2a + 3b - 4c)
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
