Question

tìm x, y là các số tự nhiên biết: 8(x-2013)²+y²=25

Answer 1

Ta có: 8.(x-2013)²+y²=25

=>y²=25-8.(x-2013)²

Vì \(\left(x-2013\right)^2\ge0=>8.\left(x-2013\right)^2\ge0=>25-8.\left(x-2013\right)^2\le25-0\)

=>\(y^2\le25=>y\le5\)

=>\(y\in\left\{1,2,3,4,5\right\}=>y^2\in\left\{1,4,9,16,25\right\}\)

Vì 25:8 dư 1, 8.(x-2013)² chia 8 dư 0

=>25-8.(x-2013)² chia 8 dư 1

=>y² chia 8 dư 1

mà \(y^2\in\left\{1,4,9,16,25\right\}\)

=>y²=25=>y=5

25-8.(x-2013)²=25

=>8.(x-2013)²=0

=>(x-2013)²⁼⁰

=>x-2013=0

=>x=2013

Vậy x=2013, y=5