bonjour

f (x) = ( 4 x² - 4 x + 1 ) - ( x - 3 )²

f ( x) = 4 x² - 4 x + 1 - ( x² - 6 x + 9 )

f (x) = 4 x² - 4 x + 1 - x² + 6 x - 9

f (x ) =  3 x² + 2 x - 8

f (x) = (  ( 2 x - 1 )² - ( x - 3 ) ²

f ( x) = ( 2 x - 1 + x - 3 ) ( 2 x - 1 - x + 3 )

f (x) = ( 3 x - 4 ) ( x + 2 )

f ( 1 + √2)  = 3 ( 1 + √2 )  *  ( 1 + √2)

                =  ( 3 + 3 √2)  ( 1 + √2)

                = 3 + 3 √2 + 3 √2 + 6

                 9 + 6 √2

f ( x) = 0

( 3 x - 4 ) ( x + 2 ) = 0

soit  x =  4/3

soit x =  - 2

f (x) = 2 x + 1

( 3 x- 4 ) ( x +2 ) = 2 x + 1

3 x² + 6 x - 4 x - 8 = 2 x + 1

3 x²  + 2 x - 2 x =  1 + 8

3 x² =  9

x²  = 3

x =  √ 3 ou - √3

g (x) = ( 3 x-  4 )²

g ( - 1/3 ) = (  - 3 /3 - 4 )² =   ( 1 - 4 )² =  ( - 3 )² = 9

f (x) = g (x)

( 4 x² - 4 x + 1 ) - ( x - 3 )² =  ( 3 x - 4 )²

(  2 x - 1  + x - 3 ) ( 2 x - 1 - x + 3 ) = ( 3 x  - 4 )²

( 3 x - 4 ) ( x + 2 ) = ( 3 x- 4  )²

( 3 x - 4 ) ( x + 2 ) - ( 3 x - 4 ) ² = 0

( 3 x - 4 ) ( x + 2 - 3 x + 2 ) = 0

( 3 x - 4 ) ( - 2 x + 4 ) = 0

x =  4/3 ou  x = 2

f (x ) = g (x)  pour x  = 4/3 et - 2