Question

If $49x^2-b=(7x+\frac{1}{2})(7x-\frac{1}{2}),$ then the value of $b$ is __.

• A. $0$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{1}{4}$

We have: $49x^2-b=(7x+\frac{1}{2})(7x-\frac{1}{2})$

Using formula: $(a+b)(a-b)=a^2-b^2$

We get: $49x^2-b=49x^2-(\frac{1}{2}{)}^2$
Comparing both the equations: $b=\frac{1}{4}$