Question

tính: 

1) |x|-x=0

2) |x|-x=2

3) 3.|x|+x=16

 

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Answer 1

\(1;\left|x\right|-x=0\)

\(\Leftrightarrow\left|x\right|=x\Rightarrow x=\pm x\)

\(\Leftrightarrow\orbr{\begin{cases}x=x\\x=-x\end{cases}\Leftrightarrow\orbr{\begin{cases}x\inℝ\\x=0\end{cases}}}\)

\(2;\left|x\right|-x=2\)

\(\Leftrightarrow\left|x\right|=2+x\Leftrightarrow x=\pm\left(x+2\right)\)

\(\Leftrightarrow\orbr{\begin{cases}x=x+2\\x=-x-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x\in\varnothing\\x+x=2\end{cases}\Leftrightarrow}\orbr{\begin{cases}x\in\varnothing\\2x=2\end{cases}\Leftrightarrow}\orbr{\begin{cases}x\in\varnothing\\x=1\end{cases}}}\)

Answer 2

3) Nếu \(x\ge0\)thì \(pt\Leftrightarrow3x+x=16\)

\(\Leftrightarrow4x=16\Leftrightarrow x=4\)

Nếu \(x< 0\)thì \(pt\Leftrightarrow-3x+x=16\)

\(\Leftrightarrow-2x=16\Leftrightarrow x=-8\)

Answer 3

1) Nếu \(x\ge0\)thì \(pt\Leftrightarrow x-x=0\Leftrightarrow0=0\)

\(\Leftrightarrow pt\)thỏa mãn với mọi x.\(\inℝ\)

 Nếu \(x< 0\)thì \(pt\Leftrightarrow-x-x=0\Leftrightarrow-2x=0\Leftrightarrow x=0\)

Vậy pt thỏa mãn với mọi \(x\inℝ\)

2) Nếu \(x\ge0\)thì \(x-x=2\Leftrightarrow0=2\left(voli\right)\)

Nếu \(x< 0\)thì \(-x-x=2\Leftrightarrow-2x=2\Leftrightarrow x=-1\)

Vậy x = -1