Question

[a hi hi]

TÌM CÁC SỐ TỰ NHIÊN x , y THỎA MÃN : 

1/x + y/3 = 1/6

TÌM x : 

a) 3/4 - 2 × | 2x - 2/3  | = 1/2

b ) ( 2x + 3/5 )\(^2\) + 9/25 = 1

Answer 1

[Edogawa Conan]

\(\frac{1}{x}+\frac{y}{3}=\frac{1}{6}\)

=> \(\frac{1}{x}=\frac{1}{6}-\frac{y}{3}\)

=> \(\frac{1}{x}=\frac{1-2y}{6}\)

=> \(x\left(1-2y\right)=6\)

=> \(x;1-2y\inƯ\left(6\right)=\left\{1;2;3;6\right\}\)

Vì \(y\in N\Rightarrow1-2y\in\left\{1;3\right\}\)

                \(\Rightarrow x\in\left\{2;6\right\}\)

Lập bảng :

1 - 2y	1	3
x	6	2
y	0	-1 (loại)

Vậy ...

Answer 2

[Nguyễn Vũ Minh Hiếu]

\(\frac{3}{4}-2.\left|2x-\frac{2}{3}\right|=\frac{1}{2}\)

\(\Rightarrow2.\left|2x-\frac{2}{3}\right|=\frac{3}{4}-\frac{1}{2}\)

\(\Rightarrow2.\left|2x-\frac{2}{3}\right|=\frac{1}{4}\)

\(\Rightarrow\left|2x-\frac{2}{3}\right|=\frac{1}{4}:2\)

\(\Rightarrow\left|2x-\frac{2}{3}\right|=\frac{1}{8}\)

\(\Rightarrow\orbr{\begin{cases}2x-\frac{2}{3}=\frac{1}{8}\\2x-\frac{2}{3}=\frac{-1}{8}\end{cases}\Rightarrow}\orbr{\begin{cases}2x=\frac{1}{8}+\frac{2}{3}\\2x=\frac{-1}{8}+\frac{2}{3}\end{cases}\Rightarrow\orbr{\begin{cases}2x=\frac{19}{24}\\2x=\frac{13}{24}\end{cases}}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{19}{24}:2\\x=\frac{13}{24}:2\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{19}{48}\\x=\frac{13}{48}\end{cases}}\)

Vậy ...................................

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