Bonjour Kokka1602
A = ( 5x – 3)² – (5x – 3)(3x + 7)
1) développer et réduire et ordonner A
A = (5x – 3)² – (5x – 3)(3x + 7)
A = (5x)² - 2*5x*3 + 3²) – (5x*3x + 5x*7 - 3*3x - 3*7) (* est le signe de la multiplication)
A = (25x² - 30x + 9) – (15x² + 35x - 9x - 21)
A = (25x² - 30x + 9) – (15x² + 26x - 21)
A = 25x² - 30x + 9 – 15x² - 26x + 21
A = 25x² - 15x² - 30x - 26² + 9 + 21
A = 10x² - 56x + 30
2) factoriser A
A = (5x – 3)² – (5x – 3)(3x + 7)
A = (5x – 3)(5x - 3) – (5x – 3)(3x + 7)
A = (5x – 3)[(5x - 3) – (3x + 7)]
A = (5x – 3)(5x - 3 – 3x - 7)
A = (5x – 3)(5x - 3x – 3 - 7)
A = (5x – 3)(2x - 10)
A = 2(5x – 3)(x - 5)
3) Calculer A pour x= 5√2
(5 racine carrée de 2)
[tex]A = 10x^2 - 56x + 30\\\\A = 10\times(5\sqrt{2})^2 - 56\times5\sqrt{2} + 30[/tex]
[tex]A = 10\times5^2\times(\sqrt{2})^2 - 280\sqrt{2} + 30\\\\A = 10\times25\times2 - 280\sqrt{2} + 30[/tex]
[tex]A = 500 - 280\sqrt{2} + 30\\\\\boxed{A = 530 - 280\sqrt{2}\approx134,02}[/tex]
