Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
Advertisements
рдЙрддреНрддрд░
In the given problem, we have to find the value of `x^3 - 1/x^3`,
Given: `x - 1/x = 5`,
We shall use the identity (a − b)3 = a3 − b3 − 3ab(a − b),
Here putting, `x- 1/x = 5`,
`(x-1/x)^3 = x^3 - 1/x^3 - 3(x xx1/x)(x - 1/x)`
`(5)^3 = x^3 - 1/x^3 - 3(x xx1/x)(x - 1/x)`
`125 = x^3 - 1/x^3 - 3(x - 1/x)`
`125 = x^3 - 1/x^3 - 3xx5`
`125 = x^3 - 1/x^3 - 15`
`125 + 15 = x^3 - 1/x^3`
`140 = x^3 - 1/x^3`
Hence, the value of `x^3 - 1/x^3` is 140.
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Use suitable identity to find the following product:
(3x + 4) (3x – 5)
Factorise the following using appropriate identity:
4y2 – 4y + 1
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write in the expanded form: `(x/y + y/z + z/x)^2`
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
Simplify of the following:
(x+3)3 + (x−3)3
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
Find the following product:
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
If a + `1/a`= 6 and a ≠ 0 find :
(i) `a - 1/a (ii) a^2 - 1/a^2`
Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`
Expand the following:
(a + 4) (a + 7)
Find the squares of the following:
9m - 2n
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
Simplify:
(x + y - z)2 + (x - y + z)2
Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16
