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a: \(S=\dfrac{4\cdot6}{2}=12\left(cm^2\right)\)
b: Độ dài hai đường chéo là 8;6
Cạnh là 5cm
\(A=-2\left(x^2-\dfrac{1}{2}x\right)=-2\left(x^2-2.x.\dfrac{1}{4}+\dfrac{1}{16}-\dfrac{1}{16}\right)\)
\(=-2\left(x^2-2x.\dfrac{1}{4}+\dfrac{1}{16}\right)+\dfrac{1}{8}=-2\left(x-\dfrac{1}{4}\right)^2+\dfrac{1}{8}\le\dfrac{1}{8}\)
\(\Rightarrow A_{max}=\dfrac{1}{8}\)
(3-12x)(x-1)+(12x-8)(x+2)+x2=52
3(x-1)-12x(x-1)+12x(x+2)-8(x+2)+x2=52
3x-3-12x2+12+12x2+24x-8x-16+x2=52
(3x+24x-8x)+(12-3-16)+(12x2-12x2+x2)=52
19x-7+x2=52
x(19-x)=52+7=59
mà 59 là số ng tố nên x rỗng
Vậy x E \(\theta\)
d) \(2x^3+3x^2+3x+1=2x^3+x^2+2x^2+x+2x+1\)
\(=x^2\left(2x+1\right)+x\left(2x+1\right)+\left(2x+1\right)=\left(2x+1\right)\left(x^2+x+1\right)\)
e) \(2x^3-5x^2+5x-3=2x^3-3x^2-2x^2+3x+2x-3\)
\(=x^2\left(2x-3\right)-x\left(2x-3\right)+\left(2x-3\right)=\left(2x-3\right)\left(x^2-x+1\right)\)
\(\left\{{}\begin{matrix}\left(x+2\right)^2+\left(y-1\right)^2=x^2+y^2+7\left(1\right)\\\left(x+1\right)\left(y+2\right)=xy+5\left(2\right)\end{matrix}\right.\)
\(\left(2\right)\Leftrightarrow xy+2x+y+2=xy+5\Leftrightarrow2x+y+2=5\)
\(\Leftrightarrow y=3-2x\left(3\right)\)
\(\left(3\right)\left(1\right)\Rightarrow\left(x+2\right)^2+\left(2-2x\right)^2=x^2+\left(3-2x\right)^2+7\Rightarrow x=y=1\)
\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{3}{4}\\\dfrac{1}{6x}+\dfrac{1}{5y}=\dfrac{2}{15}\end{matrix}\right.\)\(\left(x,y\ne0\right)\) \(đặt\left\{{}\begin{matrix}\dfrac{1}{x}=a\\\dfrac{1}{y}=b\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a+b=\dfrac{3}{4}\\\dfrac{1}{6}a+\dfrac{1}{5}b=\dfrac{2}{15}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{1}{2}\\b=\dfrac{1}{4}\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=4\end{matrix}\right.\)\(\left(tm\right)\)