\(\sqrt{-x^2+4x}+2=2x\)
\(\sqrt{-x^2+4x}=2x-2\)
\(-x^2+4x=4x^2-8x+4\)
\(-x^2+4x-4x^2+8x-4=0\)
\(-5x^2-12x+4=0\)
\(5x^2-12x+4=0\)
\(x=\dfrac{-\left(-12\right)\pm\sqrt{\left(-12\right)^2-4.5.4}}{2.5}\)
\(x=\dfrac{12\pm\sqrt{144-80}}{10}\)
\(x=\dfrac{12\pm8}{10}\)
\(x=\dfrac{12+8}{10}\)\(\Leftrightarrow x=2\)
\(x=\dfrac{12-8}{10}\)\(\Leftrightarrow x=\dfrac{2}{5}\)
\(\dfrac{\sqrt{-2^2+4.2+2=2.2}}{\sqrt{-\left(\dfrac{2}{5}\right)^2+4.\dfrac{2}{5}+2}=2.\dfrac{2}{5}}\)
\(4=4\)
3,2=0,8
x=2
\(x\ne\dfrac{2}{5}\)
=> x=2
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