Question

\(\sqrt{x^2-2x+4}+\sqrt{x^2+5}=9-2x\)

Làm giúp mik bài này với ạ mik cảm mơn

Answer 1

\(\sqrt{x^2-2x+4}+\sqrt{x^2+5}=9-2x\left(đk:x\le\dfrac{9}{2}\right)\)

\(\Leftrightarrow x^2-2x+4+x^2+5+2\sqrt{\left(x^2-2x+4\right)\left(x^2+5\right)}=81-36x+4x^2\)

\(\Leftrightarrow2\sqrt{\left(x^2-2x+4\right)\left(x^2+5\right)}=2x^2-34x+72\)

\(\Leftrightarrow4\left(x^2-2x+4\right)\left(x^2+5\right)=4x^4+1156x^2+5184-136x^3+288x^2-4896x\)

\(\Leftrightarrow4x^4-8x^3+36x^2-40x+80=4x^4-136x^3+1444x^2-4896x+5184\)

\(\Leftrightarrow128x^3-1408x^2+4856x-5104=0\)

\(\Leftrightarrow128x^2\left(x-2\right)-1152x\left(x-2\right)+2552\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(128x^2-1152x+2552\right)=0\)

\(\Leftrightarrow x=2\left(tm\right)\)(do \(128x^2-1152x+2552>0\))