香港數學競賽題目
已有答案,求步驟,thx
1.
若x^1/2 + x^-1/2 = 3 及 b = (x^3/2 + x^-3/2 -3) / (x^2 + x^-2 -2). 求b
答案為1/3
2.
若B^1/2003 = 2003, C是B的個位數, 求C的值
答案為7
回答 (3)
1.若x^(1/2)+x^(-1/2)=3 及 b=[x^(3/2)+x^(-3/2)-3] /[x^2 + x^(-2)-2] 求b
Sol
x^(1/2)+x^(-1/2)=3
x+2+1/x=9
x+1/x=7
x^2+2+x^(-2)=49
x^2+x^(-2)=47
x^(1/2)+x^(-1/2)=3
x^(3/2)+3(x^(1/2)+x^(-1/2))+x^(-3/2)=27
x^(3/2)+(x^(-3/2)+3*3=27
x^(3/2)+x^(-3/2)=18
b=(18-3)/(47-2)=15/45=1/3
2.若B^(1/2003)=2003,C是B的個位數, 求C的值
Sol
B^(1/2003)=2003
[B^(1/2003)]^2003=2003^2003
B=2003^2003
2003^2003
=>3^2003
=>[(3^4)^500]*3^3
=>(81)^500*27
=>(1^500)*7
=7
收錄日期: 2021-04-12 11:00:37
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091125000051KK00549
檢視 Wayback Machine 備份