Réponses

2013-12-05T20:17:07+01:00
Bonsoir,

a) Vrai.

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

b) Vrai car 

(x+1)(4-x)=4x-x^2+4-x\\\\(x+1)(4-x)=-x^2+3x+4

et

\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

c) Faux car

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}

Donc  \\\\2x+1+\dfrac{1}{x}\neq\dfrac{2x^2+2}{x}