Question

Có bao nhiêu cặp \(\dfrac{a}{2}+\dfrac{b}{3}=\dfrac{a+b}{5}\)

Answer 1

Ta có:

\(\dfrac{a}{2}+\dfrac{b}{3}=\dfrac{3a}{2.3}+\dfrac{2b}{2.3}=\dfrac{3a+2b}{6}\)

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

\(\Rightarrow6\left(a+b\right)=5\left(3a+2b\right)\\ \Rightarrow6a+6b=15a+10b\\ \Rightarrow15a-6a=6b-10b\\ \Rightarrow9a=-4b\Rightarrow\dfrac{a}{b}=-\dfrac{4}{9}\)

\(\Rightarrow a=-4;b=9\)

\(\Rightarrow\left(a;b\right)\in\left\{\left(-4;9\right);\left(-4.2;9.2\right);\left(-4.3;9.3\right);\left(-4.4;9.4\right);...\right\}\)

Vậy, có vô số cặp \(\left(a;b\right)\) thỏa mãn yêu cầu đề bài

Answer 2

chịu

Answer 3

khos lắm

Answer 4

sao khó thế

Answer 5

Có vô số cặp.

Answer 6

a=b=0