Question

2002X*3=2003Y*3=2004Z*3,XYZ＞0,√2002X*3+2003Y*3+2004Z*3=√2002

Answer 1

1X+1Y+1Z最后等于√3

∵2002X*3=2003Y*3=2004Z*3 ∴X*3＞Y*3＞Z*3

∵XYZ＞0 ∴X＞Y＞Z＞0

∴√2002X*3+2003Y*3+2004Z*3＝√2002X*3×3＝√2002+√2003+√2004 ∴√2002X*3×3＝√2002+√2003+√2004

∴√X*3＝(√2002+√2003+√2004)(√2002×3)

∵X＞0 ∴X＝(√2002+√2003+√2004)(√2002×3)

由上可知Y＝(√2002+√2003+√2004)(√2003×3)

Z＝(√2002+√2003+√2004)(√2004×3)

1X+1Y+1Z=(√2002×3)(√2002+√2003+√2004)+(√2003×3) (√2002+√2003+√2004)+(√2004×3)(√2002+√2003+√2004)+

∴1X+1Y+1Z＝√3×(√2002+√2003+√2004)(√2002+√2003+√2004)