因?yàn)?00/(r+10)=200/r-1/1
所以200/(r+10)
=200/r - 1/1
=200/r - r×(1/1)
=200/r - r/r
=200-r/r
即200/(r+10) = 200-r/r,兩邊同時(shí)減去200-r/r得
200/(r+10) - 200-r/r = 0
通分得
200/(r+10) - 200-r/r
= 200r/(r+10)r - (r+10)(200-r)/(r+10)r
= [200r-(r+10)(200-r)]/(r+10)r
= [200r-(200r+2000-r^2-10r)]/(r+10)r
= r^2+10r-2000/(r+10)r
= 0
所以r^2+10r-2000=0 且 分母(r+10)r不等于0
所以r^2+10r-2000
=r^2+10r+25-2025
=(r+5)^2-2025
=(r+5)^2-45^2
=[(r+5)+45][(r+5)-45]
=(r+50)(r-40)
=0
所以r=-50或r=40
至于為什么r不等于-50要你自己在原題中找了,說(shuō)明r=-50的解“不成立”以后,得到答案r=40.
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【注】
1) r^2表示r的平方,同樣道理(r+5)^2=(r+5)×(r+5)
2) 為了嚴(yán)謹(jǐn)可以再加上說(shuō)明為什么r=40滿(mǎn)足前面導(dǎo)出的“(r+10)r不等于0”的條件