Advertisements
Advertisements
Question
Evaluate the following using identities:
`(2x+ 1/x)^2`
Advertisements
Solution
In the given problem, we have to evaluate expressions by using identities.
Given `[2x - 1/x]^2`
We shall use the identity `(a - b)^2 = a^2 - 2ab + b^2`
Here a = 2x
`b = 1/x`
By applying identity we get
`[2x - 1/x]^2 = (2x)^2 + (1/x)^2 - 2 xx 2 xx x xx 1/x`
`= (2x xx 2x) + (1/x xx 1/x) - 2 xx 2 xx x xx 1/x`
` = 4x^2 + 1/x^2 - 4`
Hence the value of `[2x - 1/x]^2 is [4x^2 + 1/x^2 - 4]`
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
Write in the expanded form:
`(a + 2b + c)^2`
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
Find the following product:
If a + b = 7 and ab = 12, find the value of a2 + b2
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)
Expand the following:
(a + 3b)2
Evaluate the following without multiplying:
(95)2
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
