Question

tim x y nguyen duong

a, x-y+2xy=7

b,2^x+2^y=2^x+y

Answer 1

a.Ta có: x+2xy-y=7

⇌ 2x+4xy-2y=14

⇌ 2x(2y+1) - (2y+1)=13

⇌ (2y+1)(2x-1) = 13

Do x,y ∈ Z⁺⇒ 2y+1;2x-1∈ Z⁺

Và (2y+1)(2x-1) = 13

Do 2y+1>2x-1 với mọi x,y ∈ Z⁺

⇒\(\left\{{}\begin{matrix}2x-1=1\\2y+1=13\end{matrix}\right.\)⇒\(\left\{{}\begin{matrix}2x=2\\2y=12\end{matrix}\right.\)⇒\(\left\{{}\begin{matrix}x=1\text{(t/m)}\\y=6\text{(t/m)}\end{matrix}\right.\)

Vậy (x,y)∈\(\left\{\left(1,6\right)\right\}\)

b. Ta có: 2^x+2^y=2^x+y

⇌ 2^x- 2^x+y+2^y=0

⇌ -2^x(2^y-1)+(2^y-1)=0

⇌ (2^y-1)(1-2^x)=0

⇌ \(\left[{}\begin{matrix}2^y-1=0\\1-2^x=0\end{matrix}\right.\) ⇒\(\left[{}\begin{matrix}2^y=1\\-2^x=-1\end{matrix}\right.\text{⇒}\left[{}\begin{matrix}y=0\text{(L)}\\x=0\text{(L)}\end{matrix}\right.\)

Vậy không tìm được các cặp (x,y) thỏa mãn bài toán