Réponse :
bonjour,
E = 4x² - 49
= (2x)² - 7²
= (2x - 7)(2x + 7 )
F = (2x-7)(-5x + 9) + 4x² - 49
= 2x ×(-5x) +9 ×2x - 7 ×(-5x) - 7 ×9 + 4x² - 49
= -10x² + 18x +35x - 63 + 4x² - 49
= -6x² + 53x - 112
F = (2x-7)(-5x + 9) + 4x² - 49
avec x = 1
= (2×1-7)(-5×1 + 9) + 4×1² - 49
= (-5)× 4 + 4 - 49
= -20+4 - 49
= -65
avec x = 1/2
F = (2×1/2 -7)(-5×1/2 + 9) + 4×(1/2)² - 49
= (-6) × ( -2.5 + 9 ) + 4×0.25 - 49
= (-6) × 6.5 + 1- 49
= - 39 + 1 - 49
= -87
avec x = √2
F = (2×√2-7)(-5×√2 + 9) + 4×(√2)² - 49
= ( 2√2 - 7 ) ( -5√2 + 9 ) + 4×2 - 49
= 2√2× (-5√2) + 2√2 ×9 - 7×(-5√2) - 7×9 + 8 - 49
= -20 + 18√2 +35√2 - 63 +8 - 49
= -20 - 63 - 49 + 8 +18√2 +35√2
= -124 + 53√2
F = (2x-7)(-5x + 9) + 4x^2 - 49
on factorise F
= (2x-7)(-5x + 9) + (2x)² - 7²
= (2x-7)(-5x + 9) + ( 2x - 7)(2x + 7)
= ( 2x - 7 ) ( -5x + 9 + 2x +7 )
=(2x-7)(-3x + 16)
F = 0
on utilise la forme la plus developpee de F :
(2x-7)(-3x + 16) = 0
2x - 7 = 0 ou - 3x + 16 = 0
2x = 7 -3x = -16
x = 7/2 x = -16/-3
x = 16/3
voila : )
