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Question
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
Options
0
`1/sqrt(2)`
`1/4`
`1/2`
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Solution
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is `underlinebb(1/4)`.
Explanation:
Given, `(49x^2 - b) = (7x + 1/2)(7x - 1/2)`
⇒ `[49x^2 - (sqrt(b))^2] = [(7x)^2 - (1/2)^2]` ...[Using identity, (a + b)(a – b) = a2 – b2]
⇒ `49x^2 - (sqrt(b))^2 = 49x^2 - (1/2)^2`
⇒ `-(sqrt(b))^2 = -(1/2)^2`
⇒ `(sqrt(b))^2 = (1/2)^2` ...[Multiplying both sides by –1]
∴ `b = 1/4`
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