Question

solve the following equations by factorization method : 4x2-4a2x+(a4-b4)=0​

Answer 1

AnsWer :

x = a² - b²/ 2 and x = a² + b²/ 2

Solution :

We have equation,

$\tt\dagger \: \: 4 {x}^{2} - 4 {a}^{2} x + ( {a}^{4} - {b}^{4} ) = 0.$

$\tt \mapsto 4 {x}^{2} - 4 {a}^{2} x + {a}^{4} - {b}^{4} = 0.$

$\tt\mapsto {(2x)}^{2} + { ({a}^{2} )}^{2} - 2(2x)( {a}^{2} ) - {b}^{4} =0 .$

$\tt\mapsto {(2x - {a}^{2}) }^{2} - {b}^{4} = 0.$

$\tt\mapsto {(2x - {a}^{2}) }^{2} - {( {b}^{2} )}^{2} = 0.$

$\tt\mapsto (2x - {a}^{2} + {b}^{2} )(2x - {a}^{2} - {b}^{2} ) = 0.$

Either,

$\tt\mapsto 2x - {a}^{2} + {b}^{2} = 0.$

$\tt\mapsto x = \frac{ {a}^{2} - {b}^{2} }{2} .$

Or,

$\tt\mapsto 2x - {a}^{2} - {b}^{2} = 0.$

$\tt\mapsto x = \frac{ {a}^{2} + {b}^{2} }{2} .$

Therefore, the value of x be a²- b²/2 and a² + b² /2.

$\rule{150}1$

Some Required Formula :

• a² - b² = ( a + b ) ( a - b ).
• (a - b )² = a² + b² - 2ab.