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Ta có: \(\frac{9}{56}<\frac{a}{8}<\frac{b}{7}<\frac{13}{28}\)
=> \(\frac{9}{56}<\frac{7a}{56}<\frac{8b}{56}<\frac{26}{56}\)
Nếu \(a=2\)thì \(b=3\)
Ta có : \(\frac{9}{56}<\frac{a}{8}<\frac{b}{7}<\frac{13}{28}\)
=> \(\frac{9}{56}<\frac{7a}{56}<\frac{8b}{56}<\frac{26}{56}\)
=> \(9<7a<8b<26\)
Vì a, b ∈ Z => 7a, 8b ∈ Z
=> 7a, 8b ∈ { 10 ; 11 ; 12 ; 13 ; 14 ; 15 ; 16 ; 17 ; 18 ; 19 ; 20 ; 21 ; 22 ; 23 ; 24 ; 25 }
=> 7a ∈ { 14 ; 21 } ; 8b ∈ { 16 ; 24 }
- Khi 7a = 14 => a = 2
- Khi 7a = 21 => a = 3
- Khi 8b = 16 => b = 2
- Khi 8b = 24 => b = 3
\(\frac{9}{56}<\frac{7.a}{7.8}<\frac{8.a}{7.8}<\frac{13.2}{28.2}\Leftrightarrow\frac{9}{56}<\frac{7a}{56}<\frac{8a}{56}<\frac{26}{56}\)
Hay
9 < 7a < 8b <26
=> a = 2 ; b= 3
a) \(\left(x+\frac{1}{4}\right)^2+\frac{11}{25}=\frac{18}{25}\)
\(\Rightarrow\left(x+\frac{1}{4}\right)^2=\frac{7}{25}\)
\(\Rightarrow\) Không có x
a/ \(\frac{x+2}{27}=\frac{x}{9}\)
=> 9(x + 2) = 27x
=> 9x + 18 = 27x
=> 9x + 18 - 27x = 0
=> 9x - 27x + 18 = 0
=> -18x = -18
=> x = 1
b/ \(\frac{-7}{x}=\frac{21}{34-x}\)
=> -7(34 - x) = 21x
=> -238 + 7x = 21x
=> 21x - 7x = -238
=> -14x = 238
=> x = -17
c) \(\frac{-8}{15}< \frac{x}{40}< \frac{-7}{15}\)
Ta có BCNN(15,40,15) = 120
=> \(\frac{-64}{120}< \frac{3x}{120}< \frac{-56}{120}\)
=> -64 < 3x < -56
=> x \(\in\){ -19;-20;-21}
Câu d tương tự
\(\frac{3}{x-5}=-\frac{4}{x+2}\)
\(\Leftrightarrow3\left(x+2\right)=-4\left(x-5\right)\)
\(\Leftrightarrow3x+6=-4x+20\)
\(\Leftrightarrow7x=14\)
\(\Leftrightarrow x=2\)
\(\frac{x}{-2}=-\frac{8}{x}\)
\(\Leftrightarrow x^2=16\)
\(\Leftrightarrow x=\pm4\)
\(-\frac{2}{x}=\frac{y}{3}\)
\(\Leftrightarrow xy=-6\)
\(\Leftrightarrow x;y\inƯ\left(-6\right)=\left\{\pm1;\pm2;\pm3;\pm6\right\}\)
Xét bảng
x | 1 | -1 | 2 | -2 | 3 | -3 | 6 | -1 |
y | -6 | 6 | -3 | 3 | -2 | 2 | -1 | 6 |
Vậy.................
\(\frac{2x-9}{240}=\frac{39}{80}\)
\(\Leftrightarrow2x-9=\frac{240.39}{80}\)
\(\Leftrightarrow2x-9=117\)
\(\Leftrightarrow2x=126\)
\(\Leftrightarrow x=63\)
\(\frac{-9}{56}< \frac{x}{7}< \frac{13}{-28}\Rightarrow\frac{-9}{56}< \frac{8x}{56}< \frac{-26}{56}\Rightarrow-9< 8x< -26\Rightarrow\)vô lí
vậy không tồn tại x
cảm ơn nhé bạn