Question

If 49x^2 - b = (7x+1/2)(7x-1/2), then find the value of b.

Answer 1

Given:

`49x^2-b=(7x+(1)/(2))(7x-(1)/(2))`

To find the value of b:

Using the identity,

`(a+b)(a-b)=a^2-b^2`

So, the given expression can be written as,

`\begin{gathered} 49x^2-b=(7x)^2-((1)/(2))^2 \\ 49x^2-b=49x^2-(1)/(4) \\ -b=49x^2-(1)/(4)-49x^2 \\ -b=-(1)/(4) \\ b=(1)/(4) \end{gathered}`

Hence, the value of b is,

`(1)/(4)`