Question

Giải phương trình: \(\sqrt{2x+3}+\sqrt{2x+\text{2}}=1\)

Answer 1

Answer 2

ĐK: x≥-1

Ta có: \(\sqrt{2x+3}+\sqrt{2x+2}=1\)

     \(\Leftrightarrow4x+5+2\sqrt{\left(2x+3\right)\left(2x+2\right)}=1\)

     \(\Leftrightarrow\sqrt{4x^2+10x+6}=-2x-2\)                           ĐK:x≤1

     \(\Leftrightarrow4x^2+10x+6=4x^2+8x+4\)

     \(\Leftrightarrow2x=-2\Leftrightarrow x=-1\left(tm\right)\)

Answer 3

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

<=> \(\sqrt{2x+3}=1-\sqrt{2x+2}\)

<=> 2x + 3 = (1 - \(\sqrt{2x+2}\))²

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

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

<=> \(2\sqrt{2x+2}\) = 0

<=> \(\sqrt{2x+2}\) = 0

<=> 2x + 2 = 0

<=> 2x = -2

<=> x = -1

Answer 4

ko có gì