Salut, aidez moi slvp c urgent pour demain: soit x=(3+2racine de 7)2 et y=(3-2racine de 7)2 1-calcule et simplifie x et y? 2- calcule: x+y ; x-y et x/y? 3-donne

Bonjour Hayatybeks9 

[tex]1)\ x=(3+2\sqrt{7})^2\\\\x=3^2+2\times3\times2\sqrt{7}+(2\sqrt{7})^2[/tex]

[tex]x=9+12\sqrt{7}+4\times7\\\\x=9+12\sqrt{7}+28[/tex]

[tex]\boxed{x=37+12\sqrt{7}}[/tex]

[tex]y=(3-2\sqrt{7})^2\\\\y=3^2-2\times3\times2\sqrt{7}+(2\sqrt{7})^2[/tex]

[tex]y=9-12\sqrt{7}+4\times7\\\\y=9-12\sqrt{7}+28[/tex]

[tex]\boxed{y=37-12\sqrt{7}}[/tex]

[tex]2)\ x+y=(37+12\sqrt{7})+(37-12\sqrt{7})\\\\\boxed{x+y=74}[/tex]

[tex]x-y=(37+12\sqrt{7})-(37-12\sqrt{7})\\\\x-y=37+12\sqrt{7}-37+12\sqrt{7}\\\\[/tex]

[tex]\boxed{x-y=24\sqrt{7}}[/tex]

[tex]\dfrac{x}{y}=\dfrac{37+12\sqrt{7}}{37-12\sqrt{7}}[/tex]

[tex]\dfrac{x}{y}=\dfrac{(37+12\sqrt{7})(37+12\sqrt{7})}{(37-12\sqrt{7})(37+12\sqrt{7})}[/tex]

[tex]\dfrac{x}{y}=\dfrac{(37+12\sqrt{7})^2}{37^2-(12\sqrt{7})^2}[/tex]

[tex]\dfrac{x}{y}=\dfrac{37^2+2\times37\times12\sqrt{7}+(12\sqrt{7})^2}{1369-12^2\times7}[/tex]

[tex]\dfrac{x}{y}=\dfrac{1369+888\sqrt{7}+12^2\times7}{1369-1008}[/tex]

[tex]\dfrac{x}{y}=\dfrac{1369+888\sqrt{7}+1008}{361}[/tex]

[tex]\dfrac{x}{y}=\dfrac{2377+888\sqrt{7}}{361}[/tex]

[tex]\boxed{\dfrac{x}{y}=\dfrac{2377}{361}+\dfrac{888\sqrt{7}}{361}}[/tex]

[tex]3)\ \boxed{x+y=74}\\\\x-y=24\sqrt{7}\approx24\times2,645[/tex]

[tex]\boxed{x-y\approx63,48}[/tex]