Question:
\[ 9x^2-b=(3x+\frac{1}{2})(3x-\frac{1}{2}) \]
(a) 0
(b) \(\frac{1}{\sqrt{2}}\)
(c) \(\frac{1}{4}\)
(d) \(\frac{1}{2}\)
Solution:
\[ (3x+\frac{1}{2})(3x-\frac{1}{2}) \]
\[ =(3x)^2-(\frac{1}{2})^2 \]
\[ =9x^2-\frac{1}{4} \]
\[ 9x^2-b=9x^2-\frac{1}{4} \]
\[ b=\frac{1}{4} \]
\[ \boxed{\frac{1}{4}} \]