Question

tìm số hữu tỉ x biết:

x+1/10 + x=1/11 + x=1/12 = x+1/13 + x+1/14

Answer 1

Ta có : \(\dfrac{x+1}{10}+\dfrac{x+1}{11}+\dfrac{x+1}{12}=\dfrac{x+1}{13}+\dfrac{x+1}{14}\)

\(\Rightarrow x+1\left(\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}\right)=x+1\left(\dfrac{1}{13}+\dfrac{1}{14}\right)\)

Vì \(\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}\ne\dfrac{1}{13}+\dfrac{1}{14}\)

\(\Rightarrow x+1=0\)

\(\Rightarrow x=-1\)

Answer 2

x+1/10 + x=1/11 + x=1/12 = x+1/13 + x+1/14

<=>(x+1)(1/10+1/11+1/12)=(x+1)(1/13+1/14)

<=>(x+1)(1/10+1/11+1/12-1/13-1/14)=0

<=>x+1=0( vì biểu thức 1/10+1/11+1/12-1/13-1/14 khác 0)

<=>x=-1