[tex]T_{38}=T_{39}\Rightarrow C_{75}^{37}(x^2)^{38}(\sqrt{x^2+1})^{37}=C_{75}^{38}(x^2)^{37}(\sqrt{x^2+1})^{38}[/tex]
Tinem cont de formula combinarilor complementare, din care obtinem
[tex]C_{75}^{37}=C_{75}^{75-37}=C_{75}^{38}[/tex]
si simplificam ecuatia cu [tex]C_{75}^{37}x^{74}(\sqrt{x^2+1})^{37}[/tex] si obtinem:
[tex]x^2=\sqrt{x^2+1}\Rightarrow x^4=x^2+1[/tex]
Notam [tex]x^2=y\Rightarrow y^2-y-1=0\Rightarrow y_{1,2}=\dfrac{1\pm\sqrt5}{2}[/tex] din care luam doar solutia pozitiva si avem
[tex]x^2=\dfrac{1+\sqrt5}{2}\Rightarrow x_{1,2}=\pm\sqrt{\dfrac{1+\sqrt5}{2}}[/tex]
