Advertisements
Advertisements
प्रश्न
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
विकल्प
64
14
8
2
Advertisements
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
Factorise the following using appropriate identity:
4y2 – 4y + 1
Factorise the following:
27 – 125a3 – 135a + 225a2
Factorise the following:
64a3 – 27b3 – 144a2b + 108ab2
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
Write in the expanded form:
(2a - 3b - c)2
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] =
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
Find the square of : 3a + 7b
Find the square of `(3a)/(2b) - (2b)/(3a)`.
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Evaluate: (4 − ab) (8 + ab)
Evaluate, using (a + b)(a - b)= a2 - b2.
4.9 x 5.1
If a - b = 10 and ab = 11; find a + b.
If m - n = 0.9 and mn = 0.36, find:
m + n
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
Expand the following:
(3a – 2b)3
