Advertisements
Advertisements
Question
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
Options
64
14
8
2
Advertisements
Solution
In the given problem, we have to find the value of `x^3+1/x^3`
Given `x+ 1/x = 2`
We shall use the identity `(a+b)^3 = a^3 +b^3 + 3ab(a+b)`
Here putting `x+ 1/x = 2`,
`(x+ 1/x)^3 = x^3 + 1/x^3 + 3 (x xx 1/x)(x+1/ x)`
`(2)^3 = x^3 + 1/x^3 + 3 (x xx 1/x )(2)`
` 8 =x^3 + 1/x^3 + 6`
` 8-6 = x^3 + 1/x^3`
` 2= x^3 + 1/x^3`
Hence the value of `x^3 + 1/x^3` is 2.
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 8) (x – 10)
Evaluate the following using suitable identity:
(998)3
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
Evaluate of the following:
(9.9)3
Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8
If x = 3 and y = − 1, find the values of the following using in identify:
(9y2 − 4x2) (81y4 +36x2y2 + 16x4)
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
If x + y = 9, xy = 20
find: x2 - y2.
Simplify:
(2x + y)(4x2 - 2xy + y2)
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Factorise the following:
9y2 – 66yz + 121z2
Find the following product:
(x2 – 1)(x4 + x2 + 1)
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
