Advertisements
Advertisements
Question
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
Advertisements
Solution
In the given problem, we have to find the value of `x^3 - 1/x^3`,
Given: `x - 1/x = 5`,
We shall use the identity (a − b)3 = a3 − b3 − 3ab(a − b),
Here putting, `x- 1/x = 5`,
`(x-1/x)^3 = x^3 - 1/x^3 - 3(x xx1/x)(x - 1/x)`
`(5)^3 = x^3 - 1/x^3 - 3(x xx1/x)(x - 1/x)`
`125 = x^3 - 1/x^3 - 3(x - 1/x)`
`125 = x^3 - 1/x^3 - 3xx5`
`125 = x^3 - 1/x^3 - 15`
`125 + 15 = x^3 - 1/x^3`
`140 = x^3 - 1/x^3`
Hence, the value of `x^3 - 1/x^3` is 140.
RELATED QUESTIONS
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write in the expanded form:
`(m + 2n - 5p)^2`
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
Evaluate the following:
(98)3
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
Expand the following:
(x - 3y - 2z)2
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
Using suitable identity, evaluate the following:
1033
Using suitable identity, evaluate the following:
9992
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
