Question

[khoa luu]

Tìm x,y e z⁺ sao cho: x^y+y^x=23-xy

Answer 1

[shitbo]

\(+,x=1\Rightarrow y=22-y\text{ nên }y=11\left(\text{thỏa mãn}\right)\)

\(+,x=2\Rightarrow2^y+y^2=23-2y\text{ nên }\left(y+1\right)^2+2^y=24\text{ do đó: }2^y=8;\left(y+1\right)^2=16\text{ hay }y=3\left(tm\right)\)

\(+,x\ge3\text{ thì: }x^y+y^x\le20;x^y+y^x\ge3^y+y^3\text{ nên }y=1\text{ hoặc }y=2\text{ thử lại thấy }y=1;x=11;y=2;x=3\)