Advertisements
Advertisements
Question
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
Options
0
\[\frac{1}{4}\]
- \[\frac{1}{\sqrt{2}}\]
- \[\frac{1}{2}\]
Advertisements
Solution
We have to find the value of b
Given `49a^2 - b = [7a + 1/2] [7a-1/2]`
Using identity `x^2 - y^2 = (x+y)(x-y)`
We get
`49a^2 - b = [7a+1/2] [7a - 1/2]`
`49a^2 - b = [(7a)^2 - (1/2)^2]`
`49a^2 - b = [49a^2 - 1/4]`
Equating ‘b’ on both sides we get
` -b = -1/4`
` -b = -1/4`
Hence the value of b is `1/4`.
APPEARS IN
RELATED QUESTIONS
Expand the following, using suitable identity:
(2x – y + z)2
Evaluate the following using suitable identity:
(102)3
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Evaluate following using identities:
991 ☓ 1009
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Evaluate of the following:
`(10.4)^3`
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If 3x + 4y = 16 and xy = 4, find the value of 9x2 + 16y2.
Use the direct method to evaluate the following products:
(5a + 16) (3a – 7)
Use the direct method to evaluate :
(2a+3) (2a−3)
Evaluate: (5xy − 7) (7xy + 9)
Evaluate: (6 − 5xy) (6 + 5xy)
Expand the following:
(x - 3y - 2z)2
Find the squares of the following:
(2a + 3b - 4c)
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
Expand the following:
(3a – 2b)3
