bonjour
f (x) = ( 7 x - 3 )² - ( 7 x - 3 ) ( 2 x - 5 )
f (x) = 49 x² - 42 x + 9 - ( 14 x² - 35 x - 6 x + 15 )
f ( x) = 49 x² - 42 x + 9 - 14 x² + 41 x - 15
f (x) = 35 x² - x - 6
f (x) = ( 7 x - 3 ) ( 7 x - 3 - 2 x + 5 )
f (x) = ( 7 x - 3 ) ( 5 x + 2 )
f (x) = 0
( 7 x - 3 ) ( 5 x + 2 ) = 0
donc x = 3/7 ou - 2 /5
f ( V 2 ) = ( 7 V 2 - 3 ) ( 5 V 2 + 2 )
= 35 V 4 + 14 V 2 - 15 V 2 - 6
= 70 + 14 V 2 - 15 V 2 - 6
= - V 2 + 64
f (x) = - 6
35 x² - x - 6 = - 6
35 x² - x - 6 + 6 = 0
x ( 35 x - 1 ) = 0
x = 0 ou 1/35
f (x) > 0
on a vu plus haut que s'annule en 3/7 et - 2/5
x - inf - 2/5 3/7 + inf
7 x - 3 - - 0 +
5 x + 2 - 0 + +
produit + 0 - 0 +
] - inf ; - 2/5 ] U [ 3 /7 ; + inf [
