1) x=[tex]\sqrt{2} +\sqrt{3}[/tex]
y=[tex]\sqrt{2} -\sqrt{3}[/tex]
x+y= [tex]\sqrt{2} +\sqrt{3} +\sqrt{2} -\sqrt{3}[/tex] = [tex]2\sqrt{2}[/tex]
x-y= [tex]\sqrt{2} +\sqrt{3} -\sqrt{2} -\sqrt{3}[/tex]=0
[tex](x+y)^{2} =[/tex] [tex](\sqrt{2}+\sqrt{3}) ^{2} +2(\sqrt{2} +\sqrt{3} )(\sqrt{2} -\sqrt{3} ) + ( \sqrt{2}-\sqrt{3} )^{2}[/tex]
[tex]5+2\sqrt{6} -2+5-2\sqrt{6}[/tex]=8
2) (Acolo cred că e [tex]x^{3} -x[/tex])
a) [tex]\sqrt{2} ^{3} -\sqrt{2} = 2\sqrt{2} -\sqrt{2} =\sqrt{2}[/tex]
b) x(x-1)(x+1)
c) [tex]x^{3} -x=0 => x^{3} =3 =>x=\sqrt[3]{3}[/tex]
3) a) [tex]x^{2} -2x-4x+8(=) x(x-2)*4(x-2) (=) (x-2)(x-4)[/tex]
b) x-2=0=>x=2
x-4=0=>x=4
4) a) x(x-1)
b) (x-2)(x+2)
c) [x+y+1(x-y+1)]*[x+y+1(x-y+1)]
=>(x+y+1-x+y-1)(x+y+1+x-y+1)
=>2y(2x+2)
=>2y*2(x+1)
=>2*2y*(x+1)=>4y(x+1)
5) a) [tex]x^{2} -3=0=>x^{2} =3=>x=\sqrt{3}[/tex] si x= [tex]-\sqrt{3}[/tex]
b) x=+1 si x=-1
c) [tex]x^{2} (x^{2} -4)=0=> x^{2} =0=>x=0[/tex]
si [tex]x^{2} -4=0=>x^{2} =4=>x=+2[/tex] si x=-2
