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
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Evaluate the following using identities:
(2x + y) (2x − y)
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
Write in the expanded form: (ab + bc + ca)2
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
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 a + b = 6 and ab = 20, find the value of a3 − b3
If x = −2 and y = 1, by using an identity find the value of the following
Find the following product:
(3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.
Use the direct method to evaluate the following products:
(a – 8) (a + 2)
Evaluate: (2 − z) (15 − z)
Simplify by using formula :
(a + b - c) (a - b + c)
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
Find the following product:
(x2 – 1)(x4 + x2 + 1)
