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發表 lcflcflcf 於 星期一 五月 08, 2006 11:25 pm

a+3b=2c=>a+b=2(c-b),a=2c-3b
2a^2+c^2=3b^2=>2(a+b)(a-b)=(b+c)(b-c)
∵b≠c
代入化簡得
15a=3c=5b...(a:b:c=1:3:5)
=>abc=15a^3,(a,b,c)=a

[a,b,c]=300
=abc/(a,b,c)^2=15a
a=20
b=60
c=100

[問題]求a,b,c

發表 tangpakchiu 於 星期一 五月 08, 2006 6:35 pm

#ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#SPAN style="FONT-SIZE: 24pt; FONT-FAMILY: 細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl##ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#設#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA; mso-fareast-font-family: 新細明體"#ed_cl#a,b,c∈N#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#且#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA; mso-fareast-font-family: 新細明體"#ed_cl#a+3b=2c,2a^2+c^2=3b^2#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#,又#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA; mso-fareast-font-family: 新細明體"#ed_cl#[a,b,c]=300#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#,求#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA; mso-fareast-font-family: 新細明體"#ed_cl#a,b,c#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#之值。#ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#SPAN style="FONT-SIZE: 24pt; FONT-FAMILY: 細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl##ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#SPAN style="FONT-SIZE: 24pt; FONT-FAMILY: 細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl##ed_op#SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA"#ed_cl#請列部驟。#ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#