\(5^a+143=b^2\\ \Leftrightarrow b^2-5^a=143=144-1\\ \Leftrightarrow\left\{{}\begin{matrix}b^2=144\\5^a=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=\pm12\\a=0\end{matrix}\right.\\ \Leftrightarrow\left(a;b\right)=\left\{\left(0;12\right);\left(0;-12\right)\right\}\)

\(a=0;b=12\)

Ta có: \(\frac{1}{a}\)+\(\frac{1}{b}\)=\(\frac{2}{143}\)\(\Rightarrow\)\(\frac{a+b}{ab}\)=\(\frac{2}{143}\)\(\Rightarrow\)143(a+b)=2ab (1)

Mặt khác: a-b=2\(\Rightarrow\)a=2+b (2)

Thay (2) vào (1) ta có:

143(2+b+b)=2(2+b)b\(\Leftrightarrow\)286+286b=b(4+2b)=286+286b=4b+2bb\(\Leftrightarrow\)2bb+4b-286b-286=0\(\Leftrightarrow\)2bb-282b-286=0

ta có a=11;b=13

b=13;a=11

http://olm.vn/hoi-dap/question/550384.html