Răspuns :
mai intai trebuie sa folosesti formula: [tex] (a+b)^{2} = a^{2} + b^{2} +2ab[/tex] si [tex](a-b)^{2} = a^{2} -2ab+ b^{2} [/tex]
[tex](1/ \sqrt{2}+1)^{2} =(1/ \sqrt{2})^{2} +2/ \sqrt{2} +1^{2} =1/2+2/ \sqrt{2} +1[/tex]
[tex](1/ \sqrt{2} -1)^{2} =(1/ \sqrt{2})^{2} -2/ \sqrt{2}+1 =1/2-2/ \sqrt{2} +1[/tex]
1/2+2/[tex] \sqrt{2} [/tex]+1+1/2-2/[tex] \sqrt{2} [/tex]+1-1/2=1/2+2=5/2
[tex](1/ \sqrt{2}+1)^{2} =(1/ \sqrt{2})^{2} +2/ \sqrt{2} +1^{2} =1/2+2/ \sqrt{2} +1[/tex]
[tex](1/ \sqrt{2} -1)^{2} =(1/ \sqrt{2})^{2} -2/ \sqrt{2}+1 =1/2-2/ \sqrt{2} +1[/tex]
1/2+2/[tex] \sqrt{2} [/tex]+1+1/2-2/[tex] \sqrt{2} [/tex]+1-1/2=1/2+2=5/2
( 1/√2 + 1)² + ( 1/√2 - 1)²- 1/2=(1/√2)²+2/√2+1+(1/√2)²-2/√2+1-1/2=1/2+2/√2+1+1/2-2/√2+1-1/2=1/2+1+1/2+1-1/2=1/2+1+1=1/2+2=5/2