rezolvati inecuatia combinari de 15 luate cate 8<sau egal cu combinari de 15 luate cate x-2,x€N,x>sau egal cu 2​

Răspuns:

C₁₅⁸≤C₁₅ˣ⁻²=>x-2≤15 ; x≤17

15!/8!(18-8)!≤15!/(x-2)!*[15-(x-2)]║:15!

1/8!*10!≤1/(x-2)!*(15-x+2)!=>

8!*10!≥(x-2)!(17-x)!=>

1)8!≥(x-2)!

8>x-2

8+2≥x

10≥x

x≤10=>

.x∈{0,1,2,...,10}

2)10!≥(17-x)!

10≥17-x

x≥17-10

x≥7=>

x={7,8,9...,17}

Reuninds solutiile  de  la  1)  si  2)=>

x={0,1,2,...,7,8,9,10,...17}

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