Question

[Guyn]

a)\(\sqrt{3x^2-12x+16}+\sqrt{y^2-4y+13}=5\)

b)\(x^2+4x+5=2\sqrt{2x+3}\)

Answer 1

[Nguyễn Quang Trung]

b/ \(\Rightarrow2x+3+2\sqrt{2x+3}-x^2-6x-8=0\)

Đặt \(a=\sqrt{2x+3}\left(a\ge0\right)\)

\(\left(1\right)\Rightarrow a^2+2a-x^2-6x-8=0\)

Có: \(\Delta=1+x^2+6x+8=x^2+6x+9=\left(x+3\right)^2\)

\(\Rightarrow\sqrt{\Delta}=x+3\)

\(\Rightarrow a=\frac{-1+x+3}{1}=x+2\)

hoặc \(a=\frac{-1-x-3}{1}=-x-4\)

+) Với a = x + 2 \(\Leftrightarrow\sqrt{2x+3}=x+2\left(x\ge-2\right)\) 

......... tự giải ra x

+) Với a = -x - 4  \(\Leftrightarrow\sqrt{2x+3}=-x-4\left(x\le-4\right)\)

.........tự giải ra x