Bonsoir
f(x) = (2x + 1) (x - 3) + (2x + 1) (3x + 2)
= (2x + 1) [ (x - 3) + (3x + 2) ]
= (2x + 1) (x - 3 + 3x + 2)
= (2x + 1) (4x - 1)
= 2x * 4x + 2x * (-1) + 1 * 4x + 1 * (-1)
= 8x² - 2x + 4x - 1
= 8x² + 2x - 1
f(x) = 8x²
<=> 8x² + 2x - 1 = 8x²
<=> 8x² + 2x - 1 - 8x² = 0
<=> 2x - 1 = 0
<=> 2x = 1
<=> x = 1/2
Vérification :
f(1/2) = (2 * (1 / 2) +1) ((1 / 2) - 3) + (2 * (1 / 2) + 1) (3 * (1 / 2) + 2) = 2
8 * (1 / 2)² = 2
Voilà j'espère avoir pu t'aider ^^
