Question

tìm x,y thuộc Z biết 

a)25-y²=8(x-2019)²

^{b)|2018-x|+|2019-x|+|2020-x|=2}

Answer 1

a) Ta có:\(8\left(x-2019\right)^2⋮8\Rightarrow25-y^2⋮8\)\(\left(1\right)\)

Mặt khác: \(8\left(x-2019\right)^2\ge0\Rightarrow25-y^2\ge0\)\(\left(2\right)\)

Từ\(\left(1\right),\left(2\right)\)ta có: \(y^2=1;9;25\)

Xét:\(y^2=1\Rightarrow8\left(x-2019\right)^2=24\Rightarrow\left(x-2019\right)^2=3\left(ktm\right)\)

\(y^2=9\Rightarrow8\left(x-2019\right)^2=16\Rightarrow\left(x-2019\right)^2=2\left(ktm\right)\)

\(y^2=25\Rightarrow8\left(x-2019\right)^2=0\Rightarrow\left(x-2019\right)^2=0\Rightarrow x-2019=0\Rightarrow x=2019\left(tm\right)\)

Vậy \(y=5;x=2019\)

\(y=-5;x=2019\)