Question

Giair pt sau
\(\sqrt{x^2+4-4x}=2-x\)
help

Answer 1

\(\sqrt{x^2-4x+4}=2-x\)

\(\Leftrightarrow\sqrt{\left(x-2\right)^2}=2-x\)

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

=>x-2<=0

=>x<=2

Answer 2

\(\sqrt{x^2-4x+4}=2-x\left(x\le2\right)\)

\(\Leftrightarrow\sqrt{x^2-2\cdot x\cdot2+2^2}=2-x\)

\(\Leftrightarrow\sqrt{\left(x-2\right)^2}=2-x\)

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

+) \(x-2=2-x\)

\(\Leftrightarrow x+x=2+2\)

\(\Leftrightarrow2x=4\)

\(\Leftrightarrow x=2\left(tm\right)\)

+) \(x-2=-\left(2-x\right)\)

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

\(\Leftrightarrow0=0\) (luôn đúng)

Vậy phương trình thỏa mãn với mọi \(x\le2\)