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a) \(\frac{x}{6}^2=\frac{24}{25}\)
\(\Rightarrow x^2.25=6.24\)
\(\Rightarrow x^2.25=144\)
\(\Rightarrow x^2=144\div25\)
\(\Rightarrow x^2=5,76=2,4^2=\left(-2,4^2\right)\)
\(\Rightarrow x\in\left\{2,4;-2,4\right\}\)
Vậy \(x\in\left\{2,4;-2,4\right\}\)
b) \(\frac{72-x}{7}=\frac{x-40}{9}\)
\(\Rightarrow\left(72-x\right).9=\left(x-40\right).7\)
\(\Rightarrow648-9x=7x-280\)
\(\Rightarrow\left(-280\right)-648\) \(=-9x-7x\)
\(\Rightarrow-928=-16x\)
\(\Rightarrow x=58\)
Vậy \(x=58\)
\(\frac{x-40}{9}=\frac{72-x}{7}\)
=> 7 ( x - 40 ) = 9 ( 72 - x )
7 x - 280 = 648 - 9 x
7 x + 9 x = 648 + 280
16 x = 928
x = 58
\(\frac{x-40}{9}=\frac{72-x}{7}\)
\(\Rightarrow\left(x-40\right).7=9.\left(72-x\right)\)
\(\Rightarrow648-9x=7x-280\)
\(\Rightarrow\left(-280\right)-648=\left(-9x\right)-7x\)
\(\Rightarrow-928=-16x\)
\(\Rightarrow x=58\)
=> (72 - x) . 9 = (x - 40) . 7
=> 648 - 9x = 7x - 280
=> 648 + 280 = 7x + 9x
=> 928 = 16x
=> x = 58
a.
\(\frac{x}{4}=\frac{3}{2}\)
\(x=\frac{3}{2}\times4\)
\(x=6\)
b.
\(\frac{x}{16}=\frac{9}{x}\)
\(x\times x=16\times9\)
\(x^2=144\)
\(x^2=\left(\pm12\right)^2\)
\(x=\pm12\)
Vậy \(x=12\) hoặc \(x=-12\)
c.
\(\frac{x^2}{6}=\frac{24}{25}\)
\(x^2=\frac{24}{25}\times6\)
\(x^2=\frac{144}{25}\)
\(x^2=\left(\pm\frac{12}{5}\right)^2\)
\(x=\pm\frac{12}{5}\)
Vậy \(x=\frac{12}{5}\) hoặc \(x=-\frac{12}{5}\)
d.
\(\frac{72-9}{7}=\frac{x-40}{9}\)
\(\frac{x-40}{9}=\frac{63}{7}\)
\(x-40=\frac{63}{7}\times9\)
\(x-40=81\)
\(x=81+40\)
\(x=121\)
=> (72 - x) . 9 = (x - 40) . 7
=> 648 - 9x = 7x - 280
=> (-280) - 648 = -9x - 7x
-928 = -16x
=> x = 58
=> x/5 = y/7
Áp dụng ......... bằng nhau , ta có:
x/5 = y/7 = x + y/5 + 7 =72/12 = 6
=> x = 30
=> y = 42
Ta có: \(\frac{x}{5}=\frac{y}{7}=\frac{x+y}{5+7}=\frac{72}{12}=6\)
\(\Rightarrow\frac{x}{5}=6\Rightarrow x=30;\frac{y}{7}=6\Rightarrow y=42\)
\(\text{Cách 1:}\)
\(\frac{72-x}{7}=\frac{x-40}{9}\)
=> \(\left(72-x\right)\cdot9=\left(x-40\right)\cdot7\)
=> \(648-9x=7x-280\)
=> \(648+280=7x+9x\)
=> \(16x=928\)=> \(x=928:16=58\)
\(\text{Cách 2:}\)
\(\text{Áp dụng tính chất dãy tỉ số bằng nhau, ta có:}\)
\(\frac{72-x}{7}=\frac{x-40}{9}=\frac{72-x+x-40}{7+9}=\frac{32}{16}=2\)
\(\text{Ta suy ra:}\)
\(\frac{72-x}{7}=2\)=> \(72-x=2\cdot7=14\)=> \(x=72-14=58\)
\(\text{Vậy }x=58\)