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:
(x + 4) (x + 10)
Write the following cube in expanded form:
`[x-2/3y]^3`
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
Write in the expanded form:
`(a + 2b + c)^2`
Evaluate of the following:
933 − 1073
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
Evalute : `( 7/8x + 4/5y)^2`
If a + b = 7 and ab = 10; find a - b.
If a - b = 7 and ab = 18; find a + b.
Use the direct method to evaluate :
(x+1) (x−1)
Evaluate: (2 − z) (15 − z)
Expand the following:
(x - 5) (x - 4)
Expand the following:
`(2"a" + 1/(2"a"))^2`
Simplify by using formula :
(x + y - 3) (x + y + 3)
Evaluate the following without multiplying:
(103)2
Evaluate, using (a + b)(a - b)= a2 - b2.
4.9 x 5.1
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`
Simplify:
(x + y - z)2 + (x - y + z)2
Simplify:
(2x + y)(4x2 - 2xy + y2)
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Which one of the following is a polynomial?
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
Find the following product:
(x2 – 1)(x4 + x2 + 1)
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
