Question

13?.....................

Answer 1

1/C₄ˣ-1/C₅ˣ=1/C₆ˣ

C₄ˣ=4!/[(4-x)!*x!]

C₅ˣ=5!/[(5-x)!*x!]

C₆ˣ=6!/[(6-x)!*x!]

1/C₄ˣ-1/C₅ˣ=1/C₆ˣ<=>1/4!/[(4-x)!*x!]-1/5!/[(5-x)!*x!]=1/6!/[(6-x)!*x!]<=>[(4-x)!*x!]/4!-[(5-x)!*x!]/5!=[(6-x)!*x!]/6!<=>[(4-x)!*x!]/4!-[(5-x)!*x!]/(4!*5)=[(6-x)!*x!]/(4!*5*6)<=>(4-x)!-(5-x)!/5=(6-x)!/30<=>5(4-x)!-(5-x)!=(6-x)!/6<=>30(4-x)!-6(4-x)!(5-x)=(4-x)!(5-x)(6-x)<=>30-6(5-x)=30-5x-6x+x²<=>-30+6x=-11x+x²<=>x²-17x+30=0

Δ=289-120=169

x₁,₂=(17±13)/2

x₁=(17+13)/2=30/2=15

x₂=(17-13)/2=4/2=2

S={2;15}