Question

Giải phương trình sau:\(\sqrt{5x+7}-\sqrt{x+3}=\sqrt{3x+1}\)

Answer 1

\(ĐKXĐ:x\ge\frac{-1}{3}\)

Bình phương hai vế:

\(\left(\sqrt{5x+7}-\sqrt{x+3}\right)^2=\left(\sqrt{3x+1}\right)^2\)

\(\Leftrightarrow6x+10-2\sqrt{\left(5x+7\right)\left(x+3\right)}=3x+1\)

\(\Leftrightarrow3x+9-2\sqrt{\left(5x+7\right)\left(x+3\right)}=0\)

\(\Leftrightarrow3\left(x+3\right)-2\sqrt{\left(5x+7\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\sqrt{x+3}\left(3\sqrt{x+3}-2\sqrt{5x+7}\right)=0\)

+) \(\sqrt{x+3}=0\Rightarrow x=-3\left(ktmđk\right)\)

+) \(3\sqrt{x+3}=2\sqrt{5x+7}\)

Bình phương hai vế: \(9\left(x+3\right)=4\left(5x+7\right)\)

\(\Leftrightarrow9x+27=20x+28\Leftrightarrow-11x=1\Leftrightarrow x=\frac{-1}{11}\)(ktm)

Vậy phương trình vô nghiệm

Answer 2

Nghiệm \(\frac{-1}{11}\)thỏa mãn nha, mk nhầm

Answer 3

\(-\frac{1}{11}\left(KTM\right)\)