ĐK:x>=2
Căn[(x-2)(x-1)] + Căn(x+3) = Căn(x-2) + Căn[(x-1)(x-3)]
[Căn(x-1)-1]×[Căn(x-2)-Căn(x+3)=0
TH1: Căn(x-1)-1=0
<=> Căn(x-1)=1
=> x-1=1
=> x=2 (TM)
TH2: Căn(x-2)-Căn(x+3)=0
=> x-2+2Căn[(x-2)(x+3)]+x+3=0
<=> 2x+1=2Căn[(x-2)(x+3)
=> 4x2+4x+1=4(x-2)(x+3)
<=> 4x2+4x+1=4x2+4x-24
<=> 0x=-25(vô lý)
Vậy pt có 1 nghiệm là x=2
\(\sqrt{x^2-3x+2}\)+\(\sqrt{x+3}\)=\(\sqrt{x-2}\)+\(\sqrt{x^2+2x-3}\)(dkxd x>2)
<=>\(\sqrt{\left(x-1\right)\left(x-2\right)}+\sqrt{x+3}\)=\(\sqrt{x-2}+\sqrt{\left(x+3\right)\left(x-1\right)}\)
<=>\(\sqrt{x-1}\left(\sqrt{x-2}-\sqrt{x-3}\right)-\left(\sqrt{x-2}-\sqrt{x-3}\right)=0\)
< =>\(\left(\sqrt{x-1}-1\right)\left(\sqrt{x-2}-\sqrt{x-3}\right)=0\)
den day tu lam nha ban