Bonjour,
Deux méthodes de calcul:
[tex]\boxed{(a+b)^2=a^2+2ab+b^2}\\\\\boxed{a^2-b^2=(a+b)(a-b)} [/tex]
[tex] 1)\\(u+v)^2-(u-v)^2=[(u+v)+(u-v)]*[(u+v)-(u-v)]\\=(2u)*(2v)=4uv\\2)\\(u+v)^2-(u-v)^2=(u^2+2uv+v^2)-(u^2-2uv+v^2)\\=u^2-u^2+v^2-v^2+2uv+2uv\\=4uv\\Ici,\ u=x\ et\ v=\dfrac{2}{999} \\4uv=4x*\dfrac{2}{999}=\dfrac{8x}{999}\\\\\\\dfrac{8x}{999}=\dfrac{2}{1000}\\\Longleftrightarrow\ x=\dfrac{2*999}{8*1000}\\\Longleftrightarrow\ x=\dfrac{999}{4000}\\\Longleftrightarrow\ x=0.24975 [/tex]
