Question

[Vũ Hùng Việt]

a. x² - 4x + y² - 6y + 13

b. 2x² + y² + 2xy - 6x - 2y + 5

c. x² + 2y²  - 2xy + 8y - 4x + 8  

Answer 1

[l҉o҉n҉g҉ d҉z҉]

a) x² - 4x + y² - 6y + 13

= ( x² - 4x + 4 ) + ( y² - 6y + 9 )

= ( x - 2 )² + ( y - 3 )²

b) 2x² + y² + 2xy - 6x - 2y + 5

= ( x² + 2xy + y² - 2x - 2y + 1 ) + ( x² - 4x + 4 )

= [ ( x² + 2xy + y² ) - ( 2x + 2y ) + 1 ] + ( x - 2 )²

= [ ( x + y )² - 2( x + y ) + 1² ] + ( x - 2 )²

= ( x + y - 1 )² + ( x - 2 )²

c) x² + 2y² - 2xy + 8y - 4x + 8

= ( x² - 2xy + y² - 4x + 4y + 4 ) + ( y² + 4y + 4 )

= [ ( x² - 2xy + y² ) - 2( x - y )2 + 2² ] + ( y + 2 )²

= [ ( x - y )² - 2( x - y )2 + 2² ] + ( y + 2 )²

= ( x - y - 2 )² + ( y + 2 )²