Question

Giải các phương trình sau:

a) \(x^2+4\sqrt{x+3}=3x+6\)

b) \(x+4\sqrt{x+3}+2\sqrt{3-2x}=11\)

c) \(3x^2-5x+6=2x\sqrt{x^2+x-3}\)

Answer 1

Khó ở bước biến đổi thôi

a)

\(\Leftrightarrow3x+6-x^2-4\sqrt{x+3}=0\)

\(\Leftrightarrow x+3-4\sqrt{x+3}+4-\left(x^2-2x+1\right)=\)0

\(\Leftrightarrow\left(\sqrt{x+3}-2\right)^2-\left(x-1\right)^2=0\)

\(\Leftrightarrow\left(\sqrt{x+3}-x+1\right)\left(\sqrt{x+3}+x-3\right)=0\)

b)

\(\Leftrightarrow-(x+3-4\sqrt{x+3}+4)-\left(3-2x+2\sqrt{3-2x}+1\right)=0\)

\(\Leftrightarrow-\left(\sqrt{x+3}-2\right)^2-\left(\sqrt{3-2x}+1\right)^2=0\)

c)

\(\Leftrightarrow(x^2+x-3-2x\sqrt{x^2+x-3}+x^2)+\left(x^2-6x+9\right)=0\)

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