Câu hỏi của Thuy Khuat

Question

Tìm x:

$\dfrac{x-28-124}{2011}+\dfrac{x-124-2011}{28}+\dfrac{x-2011-28}{124}=3$

Lê Gia Bảo · Accepted Answer

Đặt $A=\dfrac{x-28-124}{2011}+\dfrac{x-124-2011}{28}+\dfrac{x-2011-28}{124}=3$

$\Rightarrow\dfrac{x-28-124}{2011}-1+\dfrac{x-124-2011}{28}-1+\dfrac{x-2011-28}{124}-1=3-1-1-1$

$\Rightarrow\dfrac{x-28-124}{2011}-\dfrac{2011}{2011}+\dfrac{x-124-2011}{28}-\dfrac{28}{28}+\dfrac{x-2011-28}{124}=0$

$\Rightarrow\dfrac{x-28-124-2011}{2011}+\dfrac{x-124-2011-28}{28}+\dfrac{x-2011-29-124}{124}=0$

$\Rightarrow x-28-124-2011\left(\dfrac{1}{2011}+\dfrac{1}{28}+\dfrac{1}{124}\right)=0$

$\Rightarrow x-28-124-2011=0\Rightarrow x=2163$

Vậy x = 2163Câu trả lời: Đặt $A=\dfrac{x-28-124}{2011}+\dfrac{x-124-2011}{28}+\dfrac{x-2011-28}{124}=3$

$\Rightarrow\dfrac{x-28-124}{2011}-1+\dfrac{x-124-2011}{28}-1+\dfrac{x-2011-28}{124}-1=3-1-1-1$

$\Rightarrow\dfrac{x-28-124}{2011}-\dfrac{2011}{2011}+\dfrac{x-124-2011}{28}-\dfrac{28}{28}+\dfrac{x-2011-28}{124}=0$

$\Rightarrow\dfrac{x-28-124-2011}{2011}+\dfrac{x-124-2011-28}{28}+\dfrac{x-2011-29-124}{124}=0$

$\Rightarrow x-28-124-2011\left(\dfrac{1}{2011}+\dfrac{1}{28}+\dfrac{1}{124}\right)=0$

$\Rightarrow x-28-124-2011=0\Rightarrow x=2163$

Vậy x = 2163

Violympic toán 7