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:
`(y^2+3/2)(y^2-3/2)`
Expand the following, using suitable identity:
(x + 2y + 4z)2
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Evaluate the following using identities:
117 x 83
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write in the expanded form: (ab + bc + ca)2
Write in the expanded form: (-2x + 3y + 2z)2
Evaluate of the following:
(598)3
Find the following product:
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:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If x = −2 and y = 1, by using an identity find the value of the following
If a + b = 7 and ab = 12, find the value of a2 + b2
If a + b = 7 and ab = 10; find a - b.
Use the direct method to evaluate :
(2a+3) (2a−3)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Simplify by using formula :
(5x - 9) (5x + 9)
If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
