Question

Giải các phương trình sau:

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

b) \(\sqrt{x^2-x}\) + \(\sqrt{x^2+x-2}\) = 0

Answer 1

\(a.\sqrt{x^2-x-2}-\sqrt{x-2}=0\) ( x ≥ 2 )

⇔ \(\sqrt{\left(x+1\right)\left(x-2\right)}-\sqrt{x-2}=0\)

⇔ \(\sqrt{x-2}\left(\sqrt{x-1}-1\right)=0\)

⇔ \(x=2\left(TM\right)orx=1\left(KTM\right)\)

KL.........

\(b.\sqrt{x^2-x}+\sqrt{x^2+x-2}=0\) ( x ≥ 1 )

⇔ \(\sqrt{x\left(x-1\right)}+\sqrt{\left(x-1\right)\left(x+2\right)}=0\)

⇔ \(\sqrt{x-1}\left(\sqrt{x}+\sqrt{x+2}\right)=0\)

Do : x ≥ 1 nen : \(\sqrt{x}+2\text{ ≥}\) 0

⇔ \(x=1\left(TM\right)\)

KL..........