Question

Tìm x,y thuộc N biết 

a)xy+3x-2y=17

b)2^x+2400=7^y

 

Answer 1

\(a)xy+3x-2y=17\)

\(x.\left(y+3\right)-2y-6=17-6\)

\(x.\left(y+3\right)-2.\left(y+3\right)=11\)

\(\left(y+3\right).\left(x-2\right)=11\)

\(\Rightarrow y+3;x-2\inƯ\left(11\right)\)\(\text{Ta có bảng}\)

\(x-2\)	\(1\)	\(11\)	\(-1\)	\(-11\)
\(y+3\)	\(11\)	\(1\)	\(-11\)	\(-1\)
\(x\)	\(3\)	\(13\)	\(1\)	\(-9\)
\(y\)	\(8\)	\(-2\)	\(-14\)	\(-4\)

Mà \(x;y\in N\)\(\Rightarrow x=3;y=8\)

Answer 2

\(b)2^x+2400=7^y\)

\(\text{Ta có }:7^y\)\(\text{là số lẻ; 2400 là số chẵn}\)

\(\Rightarrow2^x\)\(\text{là số lẻ}\)

\(\Rightarrow x=0\)

\(\Rightarrow1+2400=7^y\)

\(\Rightarrow2401=7^y\)

\(\Rightarrow7^4=7^y\)

\(\Rightarrow y=4\)