Fie a=8 supra √2 si b=√2 supra 8.Aratati ca a supra √3+√2=√3-√2 supra b.

Dau coronita!!!

(8/√2)/(√3+√2)=(√3-√2)/b
b(8/√2)=(√3+√2)(√3-√2)
b=(√3+√2)(√3-√2)/(8/√2)=
=(√3²-√2²)/(8/√2)=
=(3-2)/(8/√2)=
=1/(8/√2)=1•√2/8=√2/8

a=8/√2 =>a=8√2/2=4√2
b=√2/8

[tex] \frac{a}{ \sqrt{3} + \sqrt{2} } = \frac{ \sqrt{3}- \sqrt{2}}{b}\\\\ =\ \textgreater \ a*b=( \sqrt{3} + \sqrt{2})*( \sqrt{3} -\sqrt{2}~aplicam)\\ =\ \textgreater \ ~formula~(a-b)*(a+b)=a^2-b^2\\ 4 \sqrt{2}* \frac{ \sqrt{2} }{8} =(\sqrt{3})^2-(\sqrt{2})^2\\\\ \frac{4*2}{8} =3-2\\ \frac{8}{8} =1\\ 1=1=\ \textgreater \ Adevarat!!![/tex]