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
Write the following cube in expanded form:
`[x-2/3y]^3`
Factorise the following:
64a3 – 27b3 – 144a2b + 108ab2
Write in the expanded form:
`(m + 2n - 5p)^2`
Simplify (2x + p - c)2 - (2x - p + c)2
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
Find the following product:
If a + b = 6 and ab = 20, find the value of a3 − b3
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
Use identities to evaluate : (97)2
If a - b = 7 and ab = 18; find a + b.
Use the direct method to evaluate :
(2+a) (2−a)
Use the direct method to evaluate :
(3b−1) (3b+1)
Evaluate: (2 − z) (15 − z)
Expand the following:
(x - 3y - 2z)2
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
Expand the following:
(4a – b + 2c)2
Expand the following:
(3a – 2b)3
Expand the following:
`(1/x + y/3)^3`
