Question

Tìm x thuộc Z

a) x . (x - 1) = 0

b) (x - 1)^2 = 100

c) x^50 = x^2

Answer 1

a) x . (x - 1) = 0

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+1=1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=0+1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)

b) (x - 1)² = 100 

<=> (x - 1)² = 10²

\(\Leftrightarrow\orbr{\begin{cases}x-1=10\\x-1=-10\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=10+1\\x=-10+1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=11\\x=-9\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=11\\x=-9\end{cases}}\)

Answer 2

a,\(x\left(x-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)

b,\(\left(x-1\right)^2=100\)

\(\Rightarrow\orbr{\begin{cases}x-1=10\\x-1=-10\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=11\\x=-9\end{cases}}\)

c,\(x^{50}=x^2\)

\(\Rightarrow x^{50}-x^2=0\)

\(\Rightarrow x^2\left(x^{48}-1\right)=0\)

\(\Rightarrow\hept{\begin{cases}x=0\\x=\pm1\end{cases}}\)

Answer 3

c,x⁵⁰=x²

x⁵⁰-x²=0

x².(x⁴⁸-1)=0

\(0=\hept{\begin{cases}x^2\\x^{48}-1\end{cases}}\)

x=-1

x=0

x=-1