Toán Lớp 9: Giải pt:
\sqrt{x-2000}+\sqrt{y-2001}+\sqrt{z-2002}=1/2(x+y+z)-3000
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Toán Lớp 9: Giải pt:
\sqrt{x-2000}+\sqrt{y-2001}+\sqrt{z-2002}=1/2(x+y+z)-3000
Comments ( 2 )
⇒2\sqrt{x-2000}+2\sqrt{y-2001}+2\sqrt{z-2002}=x+y+z+6000
⇔x+y+z-6000-2\sqrt{x-2000}-2\sqrt{y-2001}-2\sqrt{z-2002}=0
⇔(x-2000-2.\sqrt{x-2000}.1+1)+(y-2001-2.\sqrt{y-2001}.1+1)+(z-2002-2.\sqrt{z-2002}.1)=0
⇔(\sqrt{x-2000}-1)^2+(\sqrt{y-2001}-1)^2+(\sqrt{z-2002}-1)^2=0
⇒{(\sqrt{x-2000}-1=0),(\sqrt{y-2001}-1=0),(\sqrt{z-2002}-1=0):}
⇔{(\sqrt{x-2000}=1),(\sqrt{y-2001}=1),(\sqrt{z-2002}=1):}
⇔{(x-2000=1),(y-2001=1),(z-2002=1):}
⇔{(x=2001),(y=2002),(z=2003):}
Vậy {(x=2001),(y=2002),(z=2003):}