Răspunsuri

2014-06-06T22:04:01+03:00
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}

Tinem cont de formula combinarilor complementare, din care obtinem

C_{75}^{37}=C_{75}^{75-37}=C_{75}^{38}

si simplificam ecuatia cu C_{75}^{37}x^{74}(\sqrt{x^2+1})^{37}  si obtinem:

x^2=\sqrt{x^2+1}\Rightarrow x^4=x^2+1

Notam x^2=y\Rightarrow y^2-y-1=0\Rightarrow y_{1,2}=\dfrac{1\pm\sqrt5}{2}  din care luam doar solutia pozitiva si avem

x^2=\dfrac{1+\sqrt5}{2}\Rightarrow x_{1,2}=\pm\sqrt{\dfrac{1+\sqrt5}{2}}