Bonsoir,
a) Vrai.
[tex]2(x-1)^2+3=2(x^2-2x+1)+3\\\\2(x-1)^2+3=2x^2-4x+2+3\\\\2(x-1)^2+3=2x^2-4x+5[/tex]
b) Vrai car
[tex](x+1)(4-x)=4x-x^2+4-x\\\\(x+1)(4-x)=-x^2+3x+4[/tex]
et
[tex]\dfrac{25}{4}-(x-\dfrac{3}{2})^2=\dfrac{25}{4}-(x^2-3x+\dfrac{9}{4})\\\\\dfrac{25}{4}-(x-\dfrac{3}{2})^2=\dfrac{25}{4}-x^2+3x-\dfrac{9}{4}\\\\\dfrac{25}{4}-(x-\dfrac{3}{2})^2=}-x^2+3x+\dfrac{16}{4}\\\\\dfrac{25}{4}-(x-\dfrac{3}{2})^2=}-x^2+3x+4[/tex]
c) Faux car
[tex]2x+1+\dfrac{1}{x}=\dfrac{2x^2}{x}+\dfrac{x}{x}+\dfrac{1}{x}\\\\2x+1+\dfrac{1}{x}=\dfrac{2x^2+x+1}{x}[/tex]
Donc [tex]\\\\2x+1+\dfrac{1}{x}\neq\dfrac{2x^2+2}{x}[/tex]
