Question

Tìm x:

p/ \(70⋮x,80⋮x,x>8\)

q/ \(x⋮12,x⋮25,x⋮30,0< x< 500\)

Answer 1

p) Để \(\begin{cases}70⋮x\\80⋮x\end{cases}\)

<=> x \(\in\) ƯC(70;80)

Ta có : 70 = 2 . 5 . 7

             80 = 2⁴ . 5

=> ƯCLN(70;80) = 2 . 5 = 10

=> ƯC(70;80) = Ư(10) = { - 10 ; - 5 ; - 2 ; - 1 ; 1 ; 2 ; 5 ; 10 }

Vì x > 8

=> x \(\in\) { 10 }

q) Để \(\begin{cases}x⋮12\\x⋮25\\x⋮30\end{cases}\)

<=> x \(\in\) BC(12;25;30)

Ta có : 12 = 2² . 3

            25 = 5²

           30 = 2 . 3 . 5

=> BCNN(12;25;30) = 2² . 5² . 3 = 300

=> BC(12;25;30) = B(300) = { 0 ; 300 ; 600 ; ... }

Vì 0 < x < 500

=> x \(\in\) { 300 }

Answer 2

\(70⋮x,80⋮x\Rightarrow x\inƯC\left(70;80\right)=\left\{\pm1;\pm2;\pm5;\pm10\right\}\)

Vì x > 8 nên \(x=10\)

\(x⋮12,x⋮25,x⋮30\Rightarrow x\in BC\left(12;25;30\right)=\left\{0;\pm300;\pm600;...\right\}\)

Vì \(0< x< 500\) nên \(x=300\)