Given:
[tex]49x^2-b=(7x+\frac{1}{2})(7x-\frac{1}{2})[/tex]To find the value of b:
Using the identity,
[tex](a+b)(a-b)=a^2-b^2[/tex]So, the given expression can be written as,
[tex]\begin{gathered} 49x^2-b=(7x)^2-(\frac{1}{2})^2 \\ 49x^2-b=49x^2-\frac{1}{4} \\ -b=49x^2-\frac{1}{4}-49x^2 \\ -b=-\frac{1}{4} \\ b=\frac{1}{4} \end{gathered}[/tex]Hence, the value of b is,
[tex]\frac{1}{4}[/tex]
