Question

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

Answer 1

The value of 'b' is 0.25

Answer 2

$\displaystyle \sf{ If \: 49 {x}^{2} - b = \bigg( 7x + \frac{1}{2} \bigg)\bigg( 7x - \frac{1}{2} \bigg)} \: \: then \: \: b = \frac{1}{4}$

Given :

$\displaystyle \sf{ 49 {x}^{2} - b = \bigg( 7x + \frac{1}{2} \bigg)\bigg( 7x - \frac{1}{2} \bigg)}$

To find :

The value of b

Formula :

a² - b² = ( a + b ) ( a - b )

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

$\displaystyle \sf{ 49 {x}^{2} - b = \bigg( 7x + \frac{1}{2} \bigg)\bigg( 7x - \frac{1}{2} \bigg)}$

Step 2 of 2 :

Find the value of b

$\displaystyle \sf{ 49 {x}^{2} - b = \bigg( 7x + \frac{1}{2} \bigg)\bigg( 7x - \frac{1}{2} \bigg)}$

$\displaystyle \sf{ \implies 49 {x}^{2} - b = {\bigg( 7x \bigg)}^{2} - {\bigg( \frac{1}{2} \bigg)}^{2} }$

$\displaystyle \sf{ \implies 49 {x}^{2} - b = 49 {x}^{2} - \frac{1}{4} }$

Comparing both sides we get

$\displaystyle \sf{ b = \frac{1}{4} }$

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