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Question
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
Options
0
\[\frac{1}{4}\]
- \[\frac{1}{\sqrt{2}}\]
- \[\frac{1}{2}\]
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`.
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