Question

Giải phương trình:

\(\sqrt{x^2-22x+121}\)=2x - 15

Answer 1

\(\sqrt{x^2-22x+121}=2x-15\Leftrightarrow\sqrt{\left(x-11\right)^2}=2x-15=\left|x-11\right|=2x-15\)

th1 : \(x-11\ge0\Leftrightarrow x\ge11\)

thì \(\left|x-11\right|=2x-15\Leftrightarrow x-11=2x-15\Leftrightarrow-x=-4\Leftrightarrow x=4\left(loại\right)\)

th2 : \(x-11< 0\Leftrightarrow x< 11\)

thì \(\left|x-11\right|=2x-15\Leftrightarrow11-x=2x-15\Leftrightarrow3x=26\Leftrightarrow x=\dfrac{26}{3}\left(tmđk\right)\)

vậy \(x=\dfrac{26}{3}\)