Bonsoir,
Exercice 1
1) [tex]A=\dfrac{2-\dfrac{4}{7}}{2+\dfrac{4}{7}}\\\\A=\dfrac{\dfrac{14}{7}-\dfrac{4}{7}}{\dfrac{14}{7}+\dfrac{4}{7}}\\\\A=\dfrac{\dfrac{10}{7}}{\dfrac{18}{7}}\\\\A=\dfrac{10}{7}\times\dfrac{7}{18}[/tex]
[tex]A=\dfrac{5}{1}\times\dfrac{1}{9}\\\\\boxed{A=\dfrac{5}{9}}[/tex]
[tex]B=\dfrac{2}{5}-\dfrac{5}{4}\times\dfrac{6}{15}\\\\B=\dfrac{2}{5}-\dfrac{30}{60}\\\\B=\dfrac{2}{5}-\dfrac{1}{2}\\\\B=\dfrac{4}{10}-\dfrac{5}{10}\\\\\boxed{B=-\dfrac{1}{10}}[/tex]
2) [tex]C=-4(\sqrt{3}-1)^2\\\\C=-4[(\sqrt{3})^2-2\times\sqrt{3}\times1+1^2]\\\\C=-4(3-2\sqrt{3}+1)\\\\C=-4(4-2\sqrt{3})\\\\\boxed{C=-16+8\sqrt{3}}[/tex]
[tex]D=5(\sqrt{3}+2)^2\\\\D=5[(\sqrt{3})^2+2\times\sqrt{3}\times2+2^2]\\\\D=5(3+4\sqrt{3}+4)\\\\D=5(7+4\sqrt{3})\\\\\boxed{D=35+20\sqrt{3}}[/tex]
3) [tex]E=\dfrac{5\times10^{-3}\times(10^2)^3\times4,2}{(9-2)\times10^{-1}}\\\\E=\dfrac{5\times10^{-3}\times(10^2)^3\times4,2}{7\times10^{-1}}\\\\E=\dfrac{5\times4,2}{7}\times\dfrac{10^{-3}\times(10^2)^3}{10^{-1}}\\\\E=\dfrac{21}{7}\times\dfrac{10^{-3}\times10^{2\times3}}{10^{-1}}\\\\E=3\times\dfrac{10^{-3}\times10^{6}}{10^{-1}}\\\\E=3\times\dfrac{10^{-3+6}}{10^{-1}}[/tex]
[tex]E=3\times\dfrac{10^{3}}{10^{-1}}\\\\E=3\times10^{3-(-1)}\\\\E=3\times10^{3+1}\\\\\boxed{E=3\times10^{4}}[/tex]
Exercice 2
F = 9x² - 49 + (3x + 7)(-2x + 1)
1) Développer et réduire :
F = 9x² - 49 + (-6x² + 3x - 14x + 7)
= 9x² - 49 - 6x² + 3x - 14x + 7
= 3x² - 11x - 42
2)a) G = 9x² - 49
= (3x)² - 7²
= (3x + 7)(3x - 7)
b) Factoriser F
F = 9x² - 49 + (3x + 7)(-2x + 1)
= (3x + 7)(3x - 7) + (3x + 7)(-2x + 1)
= (3x + 7) [(3x - 7) + (-2x + 1)]
= (3x + 7) (3x - 7 - 2x + 1)
= (3x + 7) (x - 6)
