Question

Tìm a,b ϵ N t/m :

\(\frac{1}{a}+\frac{1}{b}=\frac{1}{2}\)

Answer 1

Theo đề bài ta có : 

\(\frac{1}{a}+\frac{1}{b}=\frac{1}{2}\\ \)

\(=>2\left(\frac{1}{a}+\frac{1}{b}\right)=2.\frac{1}{2}\)

\(=>\frac{2}{a}+\frac{2}{b}=1\\ =>\frac{2b}{ab}+\frac{2a}{ab}=1\\ =>\frac{2a+2b}{ab}=1\\ =>2a+2b=ab\)

\(=>ab-2a-2b=0\\ =>ab-2a-2b+4=4\\ =>a\left(b-2\right)-2\left(b-2\right)=4\\ =>\left(b-2\right)\left(a-2\right)=4\)

 

b-2	1	4	2	-1	-4	-2
a-2	4	1	2	-4	-1	-2
b	3	6	4	1	-2	0
a	6	3	4	-2	1	0

Vậy ( a;b )=(3;6),(6;3),(4;4),(-2;1),(1;-2),(0;0)

Answer 2

Theo bài ra , ta có : 

\(\frac{1}{a}+\frac{1}{b}=\frac{1}{2}\)

\(\Rightarrow\frac{b+a}{ab}=\frac{1}{2}\)

\(\Rightarrow b+a=1\) và \(ab=2\)

\(\Rightarrow a=-1\) và \(b=\frac{2}{3}\)