Question

\(\sqrt{2x+3}+\sqrt{2x+2}=1\)

Answer 1

ĐK: x≥-1

Bình phương 2 vế:

\(\Rightarrow2x+3+2x+2+2\sqrt{\left(2x+3\right)\left(2x+2\right)}=1\)

\(\Leftrightarrow4x+5+2\sqrt{4x^2+10x+6}=1\)

\(\Leftrightarrow\sqrt{4x^2+10x+6}=-2-2x\)

(bình phương 2 vế với -2- 2x ≥0 ⇔ x≤-1)

\(\Leftrightarrow4x^2+10x+6=4x^2+8x+4\Leftrightarrow2x=-2\Leftrightarrow x=-1\left(tm\right)\)