VCP equation

Solve the following equation with variations, combinations, and permutations:

4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0

Correct answer:

x =  3

Step-by-step explanation:

C2​(4)=(24​)=2!(4−2)!4!​=2⋅14⋅3​=6 4 V(2,x)−3 (x+ 12​) − x P(2) = 0 4⋅ x⋅ (x−1)−3⋅ (x+1)⋅ x/2−x⋅ 2=0  4⋅ x⋅ (x−1)−3⋅ (x+1)⋅ x/2−x⋅ 2=0 2.5x2−7.5x=0  a=2.5;b=−7.5;c=0 D=b2−4ac=7.52−4⋅2.5⋅0=56.25 D>0  x1,2​=2a−b±D​​=57.5±56.25​​ x1,2​=1.5±1.5 x1​=3 x2​=0 x>0 x=x1​=3 b=(x+12​)=(3+12​)=6 y=4⋅ 3⋅ 2⋅ 1/(1)−3⋅ b−x⋅ 2⋅ 1=4⋅ 3⋅ 2⋅ 1/1−3⋅ 6−3⋅ 2⋅ 1=0

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