Question

Tìm x, biết :

\(\left(9!-8!\right).7!.x=1^2.2^2.3^2.4^2.....8^2\)

Giải được thì tick ^^

Answer 1

\(\left(9!-8!\right).7!.x=1^2.2^2.3^2.4^2.....8^2\)

\(\Leftrightarrow\)\(8!\left(9-1\right).7!.x=\left(1.2.3.4.....8\right).\left(1.2.3.4.....8\right)\)

\(\Leftrightarrow\)\(8!.8.7!.x=8!.8!\)

\(\Leftrightarrow\)\(8!.8!.x=8!.8!\)

\(\Leftrightarrow\)\(x=\frac{8!.8!}{8!.8!}\)

\(\Leftrightarrow\)\(x=1\)

Vậy \(x=1\)

Answer 2

\(\left(9!-8!\right).7!.x=1^2.2^2.3^2.4^2.....8^2\)

\(\Leftrightarrow\)\(8!\left(9-1\right).7!.x=\left(1.2.3.4.....16\right).\left(1.2.3.4.....16\right)\)

\(\Leftrightarrow\)\(8!.8.7!.x=8!.8!\)

\(\Leftrightarrow\)\(8!.8!.x=8!.8!\)

\(\Leftrightarrow\)\(x=\frac{8!.8!}{8!.8!}\)

\(\Leftrightarrow\)\(x=1\)

Vậy \(x=1\)

Vậy