2nd class variations

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

Result

n =  50

Solution:

V2(n)=2450  n (n1)=2450 n2n2450=0  a=1;b=1;c=2450 D=b24ac=1241(2450)=9801 D>0  n1,2=b±D2a=1±98012 n1,2=1±992 n1,2=0.5±49.5 n1=50 n2=49   Factored form of the equation:  (n50)(n+49)=0 n>0 n=n1=50V_{ 2 }(n) = 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} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 1 \pm \sqrt{ 9801 } }{ 2 } \ \\ n_{1,2} = \dfrac{ 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

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