Question

x^2-2x-(4b^2-a^2)=0 solve​

Answer 1

Correct Question :

Solve :

x² - 2ax - (4b² - a² )

Solution :

x² - { 2a } x - (4b² - a² )

=> x² - ax - ax - 4b² + a²

Here we are now going to add and subtract 2bx and 2ab to this expression .

> x² - ax - ax - 4b² + a² ± 2bx ± 2ab

> Simply rearranging the terms ;

> x² - ax - 2bx - ax + a² + 2ab + 2bx - 2ab - 4b²

> x ( x - a - 2b ) - a ( x - a - 2b ) + 2b ( x - a - 2b )

=> ( x - a - 2b ) [ x - a + 2b ]

=> { x - a - 2b }{ x - a + 2b }

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Additional Information :

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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