Question

(A2-b2)x2-2 (a2-b2)x+a2-b2=0

Answer 1

$( {a}^{2} - {b}^{2} ) {x}^{2} - 2( {a}^{2} - {b}^{2} )x + {a}^{2} - {b}^{2} \\ ( {a}^{2} - {b}^{2} )( {x}^{2} - 2x + 1) \\ ( a- b)(a +b ) {(x - 1)}^{2} \\ = ( a- b)( a+ b)(x - 1)(x - 1)$
we have used two identities

Answer 2

Answer:

Step-by-step explanation:

▶ x² - 2( a² + b² )x + ( a² - b² )² = 0

a = 1

b = -2a² - 2b²

c = ( a²- b² )²

= a⁴ + b⁴ - 2a²b²

Discriminant = b² - 4ac

D = ( -2a² - 2b² )² - 4 × 1 × ( a⁴ + b⁴ - 2a²b² )

= 4a⁴ + 4b⁴ + 8 a²b² - 4a⁴ - 4b⁴ + 8a²b²

[ By cancelling like terms ]

= 16a²b²

Now,

we know that

▶ x = ( -b ± √D ) / 2a

x = { -( -2a² - 2b² ) ± √16a²b²} / 2

x = ( 2a² + 2b² ± 4ab ) / 2

x = ( 2a² + 2b² + 4ab ) /2

x = 2 ( a² + b² + ab ) /2

x = a² + b² + 2ab

x = ( 2a² + 2b² - 4ab ) /2

x = 2 ( a² + b² - 2ab ) /2

x = a² + b² - 2ab

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