Question

GPT: √5x²+14x+9−√x²−x−20=5√x+1

Answer 1

\(\text{ĐK: }x\ge5.\)

\(pt\Leftrightarrow\sqrt{5x^2+14x+9}=5\sqrt{x+1}+\sqrt{x^2-x-20}\)

\(\Leftrightarrow5x^2+14x+9=25\left(x+1\right)+x^2-x-20+10\sqrt{\left(x+1\right)\left(x-5\right)\left(x+4\right)}\)

\(\Leftrightarrow2x^2-5x+2-5\sqrt{x+4}.\sqrt{x^2-4x-5}\)

\(\Leftrightarrow2\left(x^2-4x-5\right)-5\sqrt{x^2-4x-5}.\sqrt{x+4}+3\left(x+4\right)=0\)

\(\Leftrightarrow\left(\sqrt{x^2-4x-5}-\sqrt{x+4}\right)\left(2\sqrt{x^2-4x-5}+3\sqrt{x+4}\right)=0\)

Answer 2

đề có vấn đề ko vậy bạn hình như cái căn 2 có vấn đề