Ҷои №1 барои рекламаи шумо!

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Муодиларо ҳал намоед:

\(C_{x}^{x-1}+C_{x}^{x-2}+C_{x}^{x-3}+...+C_{x}^{x-8}+C_{x}^{x-9}+C_{x}^{x-10}=1023\)

A\(=C_{x}^{x-1}+C_{x}^{x-2}+C_{x}^{x-3}+...+C_{x}^{x-8}+C_{x}^{x-9}+C_{x}^{x-10}\)

\(C_{n}^{n-k}=C_{n}^{k}\)

A\(=C_{x}^{1}+C_{x}^{2}+C_{x}^{3}+...+C_{x}^{8}+C_{x}^{9}+C_{x}^{10}\)

\(C_{x}^{1}+C_{x}^{2}+C_{x}^{3}+...+C_{x}^{8}+C_{x}^{9}+C_{x}^{10}=1023\,\,\,\,\,|+1\)

\(1+C_{x}^{1}+C_{x}^{2}+C_{x}^{3}+...+C_{x}^{8}+C_{x}^{9}+C_{x}^{10}=1024\)

\(C_{x}^{0}=1\)

\(C_{x}^{0}+C_{x}^{1}+C_{x}^{2}+C_{x}^{3}+...+C_{x}^{8}+C_{x}^{9}+C_{x}^{10}=1024\)

\(C_{x}^{0}+C_{x}^{1}+C_{x}^{2}+C_{x}^{3}+...+C_{x}^{8}+C_{x}^{9}+C_{x}^{10}=2^{10}\)

\(C_{n}^{0}+C_{n}^{1}+C_{n}^{2}+C_{n}^{3}+...+C_{n}^{n-2}+C_{n}^{n-1}+C_{n}^{n}=2^{n}\)

\(C_{x}^{0}+C_{x}^{1}+C_{x}^{2}+C_{x}^{3}+...+C_{x}^{8}+C_{x}^{9}+C_{x}^{10}=2^{10}\)

\(\Rightarrow{x = 10}\)

Муодила ҳал шуд.

Ҷавоб: x = 10