☺ Salut ☺
[tex]\blue{\rule{6cm}{1mm}}[/tex]
On donne
[tex]\pink{A} = {(3x - 5)}^{2} + (3x - 5)(7x - 4)[/tex]
[tex]\green{B} = (5x - 9)(5x + 9) - 25[/tex]
[tex]\red{C} = {(7x + 3)}^{2} - 9[/tex]
[tex]\rule{6cm}{1mm}[/tex]
a) Développons et réduisons A ; B et C :
[tex]\pink{A} = {(3x - 5)}^{2} + (3x - 5)(7x - 4)[/tex]
[tex]\pink{A} = 9{x}^{2} - 30x + 25 + 21{x}^{2} - 12x - 35x + 20[/tex]
[tex]\boxed{\boxed{\pink{A} = \green{30{x}^{2} - 77x + 45}}}[/tex]
[tex]\green{B} = (5x - 9)(5x + 9) - 25[/tex]
[tex]\green{B} = 25{x}^{2} - 81 - 25[/tex]
[tex]\boxed{\boxed{\green{B} = \blue{25{x}^{2} - 106}}}[/tex]
[tex]\red{C} = {(7x + 3)}^{2} - 9[/tex]
[tex]\red{C} = 49{x}^{2} + 42x + 9 - 9[/tex]
[tex]\boxed{\boxed{\red{C} = \green{49{x}^{2} + 42x}}}[/tex]
[tex]\rule{6cm}{1mm}[/tex]
b) Factorisons A :
[tex]\pink{A} = {(3x - 5)}^{2} + (3x - 5)(7x - 4)[/tex]
[tex]\pink{A} = (3x - 5) (3x - 5) + (3x - 5)(7x - 4)[/tex]
[tex]\pink{A} = (3x - 5) [(3x - 5) + (7x - 4)][/tex]
[tex]\pink{A} = (3x - 5) (3x - 5 + 7x - 4)[/tex]
[tex]\boxed{\boxed{\pink{A} = \green{(3x - 5) (10x - 9)}}}[/tex]
[tex]\rule{6cm}{1mm}[/tex]
c) Calculons A pour [tex]x = - 2[/tex] :
[tex]\pink{A} = 30{x}^{2} - 77x + 45[/tex]
[tex]\pink{A} = 30{(- 2)}^{2} - 77(- 2) + 45[/tex]
[tex]\boxed{\boxed{\pink{A} = \green{319}}}[/tex]
Calculons B pour [tex]x = 0[/tex]
[tex]\green{B} = 25{(0)}^{2} - 106[/tex]
[tex]\boxed{\boxed{\green{B} = \blue{ - 106}}}[/tex]
Calculons C pour [tex]x = \dfrac{1}{4}[/tex] :
[tex]\red{C} = 49{x}^{2} + 42x[/tex]
[tex]\red{C} = 49{(\dfrac{1}{4})}^{2} + 42(\dfrac{1}{4})[/tex]
[tex]\red{C} = 49 \times \dfrac{1}{16} + 42 \times \dfrac{1}{4}[/tex]
[tex]\red{C} = \dfrac{49 + 168}{16}[/tex]
[tex]\boxed{\boxed{\red{C} = \green{\dfrac{217}{16}}}}[/tex]
[tex]\blue{\rule{6cm}{1mm}}[/tex]
