YLL討論網

#ed_op#P#ed_cl#

---- 寫到:2r^2+6r^2-243=0 #ed_op#BR#ed_cl#makes me dizzy.... why can't i solve it

#ed_op#/P#ed_cl##ed_op#P#ed_cl#你的方式並沒錯... 但是..... 你 dizzy 了, 讓你在回覆提示網友時, "最高次項" 少了一次!#ed_op#/P#ed_cl##ed_op#P#ed_cl#r#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl# (2r + 3)　=　243 ← 這一行展開, 移頂後, 應如下#ed_op#BR#ed_cl#2r#ed_op#SUP#ed_cl#3#ed_op#/SUP#ed_cl# + 3r#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl# - 243 = 0#ed_op#BR#ed_cl#(r#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl# + 6r + 27)(2r - 9) = 0#ed_op#/P#ed_cl##ed_op#P#ed_cl##ed_op#/P#ed_cl##ed_op#P#ed_cl##ed_op#/P#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

2r^2+6r^2-243=0
makes me dizzy.... why can't i solve it

4.5 is right

god it!!
我在草稿紙上一直寫著
r^2(2r+3)=243
2r^2+6r^2-243=0
!!!

SCTT: giving answer only does not count money, because you can try to measure.

how have you solved that?

∠ADO=∠ABC=90° (切線垂直半徑)
∴B，C，D，O共圓 (外角等於內對角)
∴∠DOA=∠BCA (圓內接四邊形外角)
∠OAD=∠CAB (公共角)
∴△ADO∼△ABC (AAA)

CD=CB=9 (切線性質)
DO/OA=BC/CA (相似三角形的對應邊)
r/(r+3)=9/(9+k)
9r+27=9r+kr
kr=27
k=27/r ---(1)

AD/DO=AB/BC (相似三角形的對應邊)
k/r=(2r+3)/9 ---(2)

代(1)入(2)：
9k=2r²+3r
9(27/r)=2r²+3r
2r³+3r²-243=0
(2r-9)(r²+6r+27)=0
r=9/2

4.5

算出來我再對答案

(3+2r)^2+9^2=[sqrt((r+3)^2-r^2)+9]^2
4r^2+12r+90=6r+90+18sqrt(6r+9)
4r^2+6r=18sqrt(6r+9)
r(2r+3)=9sqrt(6r+9)
r(2r+3)=9sqrt3 sqrt(2r+3)
r^2(2r+3)^2=243(2r+3)
r^2(2r+3)=243
...

求圓半徑r