6xy-2x+3y=2 giúp mik với plsssss
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A=12x^3y-17xy^2
A+B=12x^3y-17xy^2-2z^3+5+3y^2-2x^4
A-B=12x^3y-17xy^2+2z^3-5-3y^2+2x^4
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Ta có : \(C=3x^2-2x+3y^2-2y+6xy-100\)
= \(\left(3x^2+3y^2+6xy\right)-\left(2x+2y\right)-100\)
=\(3\left(x+y\right)^2-2\left(x+y\right)-100\)
=\(3\cdot5^2-2\cdot5-100=-35\)
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#)Giải :
Đặt \(A=2x^2+9y^2-6xy-6x-12y+1974\)
\(\Rightarrow A=x^2+9y^2+4-6xy-12y+4x+x^2-10x+25+1945\)
\(\Rightarrow A=\left(x^2+9y^2+4-6xy-12y+4x\right)+\left(x^2-10x+25\right)+1945\)
\(\Rightarrow A=\left(x-3y+2\right)^2+\left(x-5\right)^2+1945\ge1945\)
Dâu ''='' xảy ra khi \(\hept{\begin{cases}x-5=0\\x-3y+2=0\end{cases}\Rightarrow\hept{\begin{cases}x=5\\y=\frac{7}{3}\end{cases}}}\)
Vậy GTNN của A = 1945 tại x = 5 và y = 7/3
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\(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)-\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)\)
\(=\left(2x+3y\right)\left(2x-3y\right)^2-\left(2x-3y\right)\left(2x+3y\right)^2\)
\(=\left(2x-3y\right)\left(2x+3y\right)\left(2x-3y-2x-3y\right)\)
\(=-\left(2x-3y\right)\left(2x+3y\right)\cdot6y\)
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\(a.\left(8x^4-4x^3+x^2\right):2x^2=4x^2-2x+\frac{1}{2}\)
\(b.\left(2x^4-x^3+3x^2\right):\left(-\frac{1}{3x^2}\right)=-6x^6+3x^5-9x^4\)
\(c.\left(-18x^3y^5+12x^2y^2-6xy^3\right):6xy=-3x^2y^4+2xy-y^2\)
\(d.\left(\frac{3}{4x^3y^6}+\frac{6}{5x^4y^5}-\frac{9}{10x^5y}\right):-\frac{3}{5x^3y}=-\frac{5}{4y^5}-\frac{2}{xy^4}-\frac{3}{2x^2}\)
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Đặt bthuc = A nhé
ĐKXĐ : \(2x\ne3y\)
\(A=\left[\dfrac{2x\left(4x^2+6xy+9y^2\right)}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}-\dfrac{27y^3+36xy^2}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}-\dfrac{24xy\left(2x-3y\right)}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\right]\left[\dfrac{2x\left(2x-3y\right)}{\left(2x-3y\right)}+\dfrac{9y^2+12xy}{\left(2x-3y\right)}\right]\)\(=\left[\dfrac{8x^3+12x^2y+18xy^2-27y^3-36xy^2-48x^2y+72xy^2}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\right]\left[\dfrac{4x^2-6xy+9y^2+12xy}{\left(2x-3y\right)}\right]\)
\(=\dfrac{8x^3-36x^2y+36xy^2-27y^3}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\cdot\dfrac{4x^2+6xy+9y^2}{2x-3y}\)
\(=\dfrac{\left(2x-3y\right)^3}{\left(2x-3y\right)^2}=2x-3y\)
Với x = 1/3 ; y = -2 (tmđk) thay vào A ta được : A = 2.1/3 - 3.(-2) = 20/3
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