Question

[Nguyễn Ngọc Phương Linh]

tìm tất cả các số hữu tỷ a,b,c thoả mãn

ab=3/4,bc=3/10,ca=1/10

mình cần gấp lắm mn giúp mình với

Answer 1

[Akai Haruma]

Lời giải:
Ta thấy:

$ab=\frac{3}{4}>0; bc=\frac{3}{10}>0; ca=\frac{1}{10}>0$

$\Rightarrow a,b,c>0$.

$ab=\frac{3}{4}, bc=\frac{3}{10}, ca=\frac{1}{10}$

$\Rightarrow ab.bc.ac=\frac{3}{4}.\frac{3}{10}.\frac{1}{10}$

$\Rightarrow (abc)^2=\frac{9}{400}=(\frac{3}{20})^2=(\frac{-3}{20})^2$

Do $a,b,c>0$ nên $abc>0$

$\Rightarrow abc=\frac{3}{20}$.

$a=abc:(bc)=\frac{3}{20}: \frac{3}{10}=\frac{1}{2}$

$b=abc:(ac)=\frac{3}{20}:\frac{1}{10}=\frac{3}{2}$

$c=abc:(ab)=\frac{3}{20}: \frac{3}{4}=\frac{1}{5}$

Answer 2

[HT.Phong (9A5)]

\(\dfrac{ac}{bc}=\dfrac{1}{10}:\dfrac{3}{10}=\dfrac{1}{3}\Rightarrow\dfrac{a}{b}=\dfrac{1}{3}\Rightarrow a=\dfrac{1}{3}b\)

Mà: \(ab=\dfrac{3}{4}=>\dfrac{1}{3}b\cdot b=\dfrac{3}{4}=>b^2=\dfrac{3}{4}:\dfrac{1}{3}=\dfrac{9}{4}\) 

\(\Rightarrow\left[{}\begin{matrix}b=\dfrac{3}{2}\\b=-\dfrac{3}{2}\end{matrix}\right.\)

TH1: \(b=\dfrac{3}{2}=>a=\dfrac{1}{3}\cdot\dfrac{3}{2}=\dfrac{1}{2}\)

\(\Rightarrow\dfrac{3}{2}c=\dfrac{3}{10}=>c=\dfrac{3}{10}:\dfrac{3}{2}=\dfrac{1}{5}\)

TH2: \(b=-\dfrac{3}{2}=>a=\dfrac{1}{3}\cdot\left(-\dfrac{3}{2}\right)=-\dfrac{1}{2}\)

\(\Rightarrow-\dfrac{3}{2}c=\dfrac{3}{10}=>c=\dfrac{3}{10}:-\dfrac{3}{2}=\dfrac{-1}{5}\)