Question

Solve for x:

$9 {x}^{2} - 6ax + ( {a}^{2 } - {b}^{2} ) = 0$

using the factorisation method.​

Answer 1

AnsWer :

x = a - b /3 and x = a + b /3.

Solution :

We have,

=> 9x² -6ax + a² - b² =0.

=> (3x)² -2(3x)(a) + (a)² - b² = 0.

=> ( 3x - a )² - b² = 0.

=> ( 3x - a )² - ( b )² = 0.

=> ( 3x - a + b )( 3x - a - b ) = 0.

Either,

=> 3x - a + b = 0.

=> x = a - b /3.

Or,

=> 3x - a - b = 0.

=> x = a + b /3.

$\rule{180}3$

Some Formula :

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