Question

tìm a , b thuộc Z để 5/2a=1/6+b/3 là số nguyên

tìm hộ mik nhé

Answer 1

\(\dfrac{5}{2}=\dfrac{1}{6}+\dfrac{b}{3}\)

\(\Leftrightarrow\dfrac{5}{2a}-\dfrac{1}{6}-\dfrac{b}{3}=0\)

msc : 18a

\(\Leftrightarrow\dfrac{45}{18a}-\dfrac{3a}{18a}-\dfrac{6ab}{18a}=0\)

\(\Leftrightarrow45-3a-6ab=0\)

\(\Rightarrow\left\{{}\begin{matrix}a=\dfrac{15}{1+2b}\\b=\dfrac{15}{2a}-\dfrac{1}{2}\end{matrix}\right.\)

Answer 2

\(\dfrac{5}{2a}\) hay \(\dfrac{5}{2}a\) vậy bạn?

Answer 3

\(\dfrac{5}{2a}=\dfrac{1}{6}+\dfrac{b}{3}\)

\(\Rightarrow\dfrac{15}{6a}=\dfrac{a}{6a}+\dfrac{2ab}{6a}\)

\(\Rightarrow a+2ab=15\)

\(\Rightarrow a\left(1+2b\right)=15\)

\(\Rightarrow a=\dfrac{15}{2b+1}\).

-Vì \(a,b\) nguyên nên để \(\dfrac{15}{2b+1}\) là số nguyên thì: \(15⋮\left(2b+1\right)\)

\(\Rightarrow2b+1\inƯ\left(15\right)\)

\(\Rightarrow2b+1\in\left\{1;3;5;15;-1;-3;-5;-15\right\}\)

\(\Rightarrow b\in\left\{0;1;2;7;-1;-2;-3;-8\right\}\)

*Với \(b=0\) thì \(a=\dfrac{15}{2.0+1}=15\)

*Với \(b=1\) thì \(a=\dfrac{15}{2.1+1}=5\)

*Với \(b=2\) thì \(a=\dfrac{15}{2.2+1}=3\)

*Với \(b=7\) thì \(a=\dfrac{15}{2.7+1}=1\)

*Với \(b=-1\) thì \(a=\dfrac{15}{2.\left(-1\right)+1}=-15\)

*Với \(b=-2\) thì \(a=\dfrac{15}{2.\left(-2\right)+1}=-5\)

*Với \(b=-3\) thì \(a=\dfrac{15}{2.\left(-3\right)+1}=-3\)

*Với \(b=-8\) thì \(a=\dfrac{15}{2.\left(-8\right)+1}=-1\)

Answer 4

⇔52a−16−b3=0⇔52a−16−b3=0

msc : 18a