Write the correct answer in the following: If 49x^2 -b= (7x+1 2 )… - Vidyadip

MCQ

Write the correct answer in the following:
If $49\text{x}^2 -\text{b}=\Big(7\text{x}+\frac{1}{2}\Big)\Big(7\text{x}-\frac{1}{2}\Big),$ the value of b is.

A
$0$
B
$\frac{1}{\sqrt2}$
✓
$\frac{1}{4}$
D
$\frac{1}{2}$

✓

Answer

Correct option: C.

$\frac{1}{4}$

$49\text{x}^2 -\text{b}=\Big(7\text{x}+\frac{1}{2}\Big)\Big(7\text{x}-\frac{1}{2}\Big)$
$\Rightarrow49\text{x}^2 -\text{b}=\Big(7\text{x}\Big)^2-\Big(\frac{1}{2}\Big)^2$
$49^2-\frac{1}{4} [\therefore(\text{a}+\text{b})(\text{a}-\text{b})=\text{a}^2-\text{b}^2]$
So, we get $\text{b}=\frac{1}{4}.$

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