Bài 1 : Tìm y
y x 5 + 5 = 50
y : 5 - 5 = 90
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\(y.3\dfrac{7}{12}=6\dfrac{1}{4}\)
\(y.\dfrac{43}{12}=\dfrac{25}{4}\)
\(y=\dfrac{25}{4}:\dfrac{43}{12}\)
\(y=\dfrac{25.12}{4.43}\)
\(y=\dfrac{75}{43}\)
YYY +YY+ x + x + x + 1 = 1001
3x= 1000-yyy-yy
x= (1000 - yyy - yy) :3
YY + x + 5 = 113
x= 133-5 - yy
x= 128-yy
4725 + YYY + YY + x = 5463
x= 5463- 4725 - yyy - yy
x= 738 - yyy - yy
\(2x^2+30xy=5\left(x+5y\right)\sqrt{5xy}-50y^2\)\(\left(đk:x;y\ge0\right)\)
\(\Leftrightarrow2x^2+30xy-5\left(x+5y\right)\sqrt{5xy}+50y^2=0\left(1\right)\)
\(đặt:\sqrt{5xy}=b\ge0\Rightarrow5xy=b^2\Rightarrow10xy=2b^2\)
\(x+5y=a\ge0\Rightarrow x^2+10xy+25y^2=â^2\)
\(\Rightarrow2a^2=2x^2+20xy+50y^2\)
\(\Leftrightarrow\left(1\right)\Leftrightarrow2a^2+2b^2-5ab=0\Leftrightarrow\left(2a-b\right)\left(a-2b\right)=0\Leftrightarrow\left[{}\begin{matrix}b=2a\left(2\right)\\a=2b\left(3\right)\end{matrix}\right.\)
\(\left(2\right)\Rightarrow\sqrt{5xy}=2x+10y\Leftrightarrow4x^2+35xy+100y^2=0\left(4\right)\)
\(với:y=0\) \(ko\) \(là\) \(nghiệm\)
\(với:y\ne0\Rightarrow\left(4\right)\Leftrightarrow4\left(\dfrac{x}{y}\right)^2+35\left(\dfrac{x}{y}\right)+100=0\)\(\left(vô-lí\right)\)
\(do:4\left(\dfrac{x}{y}\right)^2+35\left(\dfrac{x}{y}\right)+100>0\)
\(\left(3\right)\Rightarrow x+5y=2\sqrt{5xy}\Leftrightarrow x^2+10xy+25y^2=20xy\Leftrightarrow x^2-10xy+25y^2=0\Leftrightarrow\left(x-5y\right)^2=0\Leftrightarrow x=5y\)
\(thay:x=5y\) \(vào:2x^2+y^2=51\Rightarrow2\left(5y\right)^2+y^2-51=0\Leftrightarrow51y^2-51=0\Leftrightarrow\left[{}\begin{matrix}y=1\left(tm\right)\Rightarrow x=5\left(tm\right)\\y=-1\left(loại\right)\end{matrix}\right.\)
x + ( 9 - 8 + 7 - 6 + 5 - 4 + 3 ) = 90,28
x + 6 = 90,28
x = 90,28 - 6
x = 84,28
y x 5 + 5 = 50
y = 50 - 5 : 5
y = 9