Question

[nguyen van hieu]

CM neu x+y+z=2015 va \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2015\) thi co it nhat 1 so la 2015

Answer 1

[nguyen thi thu Thuy]

\(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2015\Leftrightarrow\frac{1}{x}+\frac{1}{y}=2015-\frac{1}{z}=\frac{z-2015}{2015z}\)

\(\Leftrightarrow\frac{x+y}{xy}=\frac{z-2015}{2015z}\Leftrightarrow2015z\left(x+y\right)=xy\left(z-2015\right)\)

\(2015z\left(2015-z\right)+\left(2015-z\right)xy=0\Leftrightarrow\left(2015-z\right)\left(2015z+xy\right)=0\)

\(\Leftrightarrow\left(2015-z\right)\left(2015\left(2015-x-y\right)+xy\right)=0\)

\(\Leftrightarrow\left(2015-z\right)\left(2015^2-2015x-2015y+xy\right)=0\)

\(\Leftrightarrow\left(2015-z\right)\left(2015-y\right)\left(2015-x\right)=0\)

vậy trong 3 số sẽ có 1 số là 2015

Answer 2

[nguyen van hieu]

nguyen thi thu thuy copy ac nhi?con doi tick nua chu!!!du sao cung thong minh nen tuj tick cho :V