Bài toán thi violympic toán tuổi thơ

L

leesyaoran2012

1/(2014-x) +1/(2015-x)+1/(2016-x)=13/12

<=> [1/(2014-x) -1/2 ] + [1/(2015-x) -1/3 ] + [1/(2016-x) -1/4 ] =0

<=> (x-2012)[1/2(2014-x) + 1/3(2015-x) + 1/4(2016-x) =0

=>

{x=2012

{1/2(2014-x) + 1/3(2015-x) + 1/4(2016-x) = 0

Đặt 2015-x =y

1/2(y-1) +1/3y +1/4(y+1) =0

=> 13y^2 - 3y - 4=0

Delta = 217 => y1,2 = (3 ± √ 217)/26

=> x1,2= 2015 -y1,2 = 2015 - (3 ± √ 217)/26
 
You must log in or register to reply here.
Top Bottom