Question

Giải phương trình

a) \(x-\sqrt{2x+3}=0\)

b) \(\sqrt{x^2+x+12}=8-x\)

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

d) \(x^2-7x+14-2\sqrt{x-3}=0\)

Answer 1

a) \(x-\sqrt{2x+3}=0\)

⇔ \(x=\sqrt{2x+3}\left(x\ge0\right)\)

⇔ \(x^2=2x+3\)

⇔ \(x^2-2x-3=0\)

⇔ x² + x - 3x - 3 = 0

⇔ x(x+1) - 3(x+1) = 0

⇔ (x-3)(x+1) = 0

⇔\(\left\{{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\Leftrightarrow x=3\)

Answer 2

a: \(\Leftrightarrow x=\sqrt{2x+3}\)

=>x^2=2x+3 và x>=0

=>x^2-2x-3=0 và x>=0

=>x=3

b: \(\Leftrightarrow\left\{{}\begin{matrix}x< =8\\x^2+x+12=x^2-16x+64\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< =8\\17x=52\end{matrix}\right.\)

=>x=52/17