Advertisements
Advertisements
प्रश्न
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
विकल्प
5
4
3
2
Advertisements
उत्तर
In the given problem, we have to find the value of `x-1/x`
Given `x^3 - 1/x^3 = 14`
We shall use the identity `(a-b)^3 = a^3 -b^3-3ab (a-b)`
`(x-1/x)^3 = x^3 - 1/x^3 - 3 xx x xx 1/x(x-1/x)`
`(x = 1/x)^3 = x^3 - 1/x^3 -3 (x-1/x)`
Put `x- 1/x = y` we get,
`(y)^3 = x^3 -1/x^3 -3(y)`
Substitute y = 2 in above equation we get,
`(2)^3 = x^3 -1/x^3 - 3 (2) `
`8 = x^3 - 1/x^3 -6`
`8+6 = x^2 -1/x^3`
`14 = x^3 - 1/x^3`
The Equation `(y )^3 = x^3 - 1/x^3 -3(y)`satisfy the condition that `x^3 - 1/x^3 = 14`
Hence the value of `x - 1 /x`is 2
APPEARS IN
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
95 × 96
Factorise the following:
64m3 – 343n3
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
Simplify (a + b + c)2 + (a - b + c)2
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
Use identities to evaluate : (101)2
Evalute : `( 7/8x + 4/5y)^2`
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate :
(2+a) (2−a)
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
Simplify by using formula :
(a + b - c) (a - b + c)
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
