Re: [中學] 請教一題對數

[mack (腦海裡依然記得妳)]

※ 引述《j19951102 (j19951102)》之銘言：
: 函數log y=log x與直線x+y-5=0共有a個交點且此a個交點的x座標總和為b，數對(a,b)=?
:        x     y
log_x y = t => t=log_y x=1/(log_x y)=1/t => t=±1
t=1=log_x y => x=y
t=-1=log_x y => xy=1

{x=y     => {x=5/2
{x+y-5=0    {y=5/2
{xy=1     => x+1/x-5=0 => x^2-5x+1=0 => x有兩根,且兩根之和=5
{x+y-5=0

共3個交點,x座標和=5+5/2=15/2
(a,b)=(3,15/2)

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