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
