Ecuatia are o greseala. In loc de 1524 trebuia 1512
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[tex]\displaystyle\\
2C_x^{x-2}+A_x^2=1512\\\\
2C_x^{x-(x-2)}+A_x^2=1512\\\\
2C_x^2+A_x^2=1512\\\\
2\cdot \frac{A_x^2}{P_2} +A_x^2=1512\\\\
2\cdot \frac{A_x^2}{2} +A_x^2=1512\\\\
A_x^2+A_x^2=1512\\\\
2A_x^2=1512\\\\
A_x^2=\frac{1512}{2} \\\\
A_x^2=756\\\\
x(x-1)=756\\\\
x^2-x-756=0\\\\
x_{12}=\frac{1\pm\sqrt{1+4\cdot 756}}{2}=\frac{1\pm\sqrt{3025}}{2}= \frac{1\pm 55}{2}\\\\
x_1= \frac{1+ 55}{2}=\frac{56}{2}=28\\\\
x_1= \frac{1- 55}{2} \notin N\\\\
\text{Solutia: }~~\boxed{x=28}[/tex]
