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
Evaluate the following product without multiplying directly:
104 × 96
Factorise the following using appropriate identity:
`x^2 - y^2/100`
Expand the following, using suitable identity:
(x + 2y + 4z)2
Evaluate the following using suitable identity:
(998)3
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Write in the expanded form: (ab + bc + ca)2
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
Evaluate of the following:
933 − 1073
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
If a − b = −8 and ab = −12, then a3 − b3 =
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
If a2 + b2 + c2 − ab − bc − ca =0, then
Find the square of `(3a)/(2b) - (2b)/(3a)`.
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
Expand the following:
(x - 5) (x - 4)
If p + q = 8 and p - q = 4, find:
p2 + q2
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
