Question

Tìm a,b \(\in\) N^* sao cho : \(\frac{1}{a}+\frac{1}{b}=\frac{1}{4}\)

Answer 1

\(\frac{1}{4}=\frac{3}{12}=\frac{2}{12}+\frac{1}{12}=\frac{1}{6}+\frac{1}{12}\)

Vậy: \(\frac{1}{a}=\frac{1}{6}\) và \(\frac{1}{b}=\frac{1}{12}\)

Answer 2

Vi 1/a + 1/b = 1/4 nen 1/a < 1/4 suy ra  a > 4 (1)

Do vai tro cua a , b binh dang nen gia su a < b suy ra 1/a > 1/b

Ta co 1/a + 1/a > 1/a + 1/b

               2/a > 1/4 = 2/8 suy ra a < 8 (2)

Tu (1) va (2) suy ra 4 < a < 8 nen a thuoc { 5 ; 6 ;7 }

+Voi a = 5 thi 1/b = 1/4 - 1/5 = 1/20, chon

+Voi a = 6 thi 1/b = 1/4 - 1/6 = 2/24 = 1/12, chon

+Voi a = 7 thi 1/b = 1/4 - 1/7 = 3/28, loai

Vay a=5,b=20 ; a=6,b=12

Answer 3

\(\frac{1}{4}=\frac{3}{12}=\frac{2}{12}+\frac{1}{12}=\frac{1}{6}+\frac{1}{12}\)

Vậy \(\frac{1}{a}=\frac{1}{6}\) và \(\frac{1}{b}=\frac{1}{12}\)

\(a=6;b=12\)