2nd class variations

From how many elements you can create 2450 variations of the second class?

Correct result:

n =  50

Solution:

$$\begin{gathered} V_2(n)=2450 \\ n\ast (n-1)=2450 \\ n\cdot (n-1)=2450 \\ {n}^2-n-2450=0 \\ a=1;b=-1;c=-2450 \\ D=b^2-4ac=1^2-4\cdot 1\cdot (-2450)=9801 \\ D>0 \\ {n}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{1\pm \sqrt{9801}}{2}} \\ {n}_{1,2}={\displaystyle \frac{1\pm 99}{2}} \\ {n}_{1,2}=0.5\pm 49.5 \\ {n}_1=50 \\ {n}_2=-49 \\ \text{ Factored form of the equation: } \\ (n-50)(n+49)=0 \\ n>0 \\ n=n_1=50 \end{gathered}$$

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