Advertisements
Advertisements
प्रश्न
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
विकल्प
64
14
8
2
उत्तर
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
संबंधित प्रश्न
Write the following cube in expanded form:
`[x-2/3y]^3`
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
Evaluate of the following:
(598)3
If \[x^4 + \frac{1}{x^4} = 194,\] find \[x^3 + \frac{1}{x^3}, x^2 + \frac{1}{x^2}\] and \[x + \frac{1}{x}\]
Find the following product:
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
Use identities to evaluate : (998)2
Use the direct method to evaluate :
(4+5x) (4−5x)
Evaluate: (2a + 0.5) (7a − 0.3)
Expand the following:
`(2"a" + 1/(2"a"))^2`
Simplify by using formula :
(x + y - 3) (x + y + 3)
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
Expand the following:
`(4 - 1/(3x))^3`
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
