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\(3x^2\left(3x^2-2y^2\right)-\left(3x^2-2y^2\right)\left(3x^2+2y^2\right)\)
\(=9x^4-6x^2y^2-9x^4+4y^4\)
\(=-6x^2y^2+4y^4\)
`A= x^2+2xy-3x^2 +2y^2+3x^2-y^2`
`= (x^2-3x^2 +3x^2) +2xy +(2y^2 -y^2)`
`= x^2 +2xy +y^2`
`=(x+y)^2`
A = \(x^2\) + 2\(xy\) - 3\(x^2\) + 2y2 + 3\(x^2\) - y2
A = (\(x^2\)- 3\(x^2\) + 3\(x^2\)) + 2\(xy\) + (2\(y^2\) - y2)
A = \(x^2\) + 2\(xy\) + y2
A = (\(x\) + y)2
\(1,\\ a,A=4x^2\left(-3x^2+1\right)+6x^2\left(2x^2-1\right)+x^2\\ A=-12x^4+4x^2+12x^2-6x^2+x^2=-x^2=-\left(-1\right)^2=-1\\ b,B=x^2\left(-2y^3-2y^2+1\right)-2y^2\left(x^2y+x^2\right)\\ B=-2x^2y^3-2x^2y^2+x^2-2x^2y^3-2x^2y^2\\ B=-4x^2y^3-4x^2y^2+x^2\\ B=-4\left(0,5\right)^2\left(-\dfrac{1}{2}\right)^3-4\left(0,5\right)^2\left(-\dfrac{1}{2}\right)^2+\left(0,5\right)^2\\ B=\dfrac{1}{8}-\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1}{8}\)
\(2,\\ a,\Leftrightarrow10x-16-12x+15=12x-16+11\\ \Leftrightarrow-14x=-4\\ \Leftrightarrow x=\dfrac{2}{7}\\ b,\Leftrightarrow12x^2-4x^3+3x^3-12x^2=8\\ \Leftrightarrow-x^3=8=-2^3\\ \Leftrightarrow x=2\\ c,\Leftrightarrow4x^2\left(4x-2\right)-x^3+8x^2=15\\ \Leftrightarrow16x^3-8x^2-x^3+8x^2=15\\ \Leftrightarrow15x^3=15\\ \Leftrightarrow x^3=1\Leftrightarrow x=1\)
\(\left(9xy-3x^2\right)\left(-2y^2-8xy\right)=-18xy^3-72x^2y^2+6x^2y^2+24x^3y=-18xy^3-66x^2y^2+24x^3y\)
\(A=\left(x^2-2xy+y^2\right)+\left(y^2-2yz+z^2\right)+\left(z^2-2xz+x^2\right)+\left(x^2+2x+1\right)+1\\ A=\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2+\left(x+1\right)^2+1\ge1\\ A_{min}=1\Leftrightarrow x=y=z=-1\)
\(3x^2-7xy+2y^2\)
\(=3x^2-6xy-xy+2y^2\)
\(=\left(3x^2-6xy\right)-\left(xy-2y^2\right)\)
\(=3x\left(x-2y\right)-y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(3x-y\right)\)
\(A=2\left(x^2-2xy+y^2\right)+\left(x^2-3x+\dfrac{9}{4}\right)+\dfrac{8067}{4}\)
\(A=2\left(x-y\right)^2+\left(x-\dfrac{3}{4}\right)^2+\dfrac{8067}{4}\ge\dfrac{8067}{4}\)
\(A_{min}=\dfrac{8067}{4}\) khi \(x=y=\dfrac{3}{2}\)
2A - (\(xy\) + 3\(x^2\) - 2y2) = \(x^2\) - 8y2 + \(xy\)
2A = \(x^2\) - 8y2 + \(xy\) + \(xy\) + 3\(x^2\) - 2y2
2A = (\(x^2\) + 3\(x^2\)) - (8y2 + 2y2) + (\(xy+xy\))
2A = 4\(x^2\) - 10y2 + 2\(xy\)
A = (4\(x^2\) - 10y2 + 2\(xy\)): 2
A = (2\(x^2\) - 5y2 + \(xy\)).2:2
A = 2\(x^2\) - 5y2 + \(xy\)
\(3x^2\cdot\left(3x^2-2y^2\right)-\left(3x^2-2y^2\right)\cdot\left(3x^2+2y^2\right)\)
\(\Leftrightarrow\left(3x^2-2y^2\right)\cdot\left(3x^2-3x^2+2y^2\right)\)
\(\Leftrightarrow2y^2\cdot\left(3x^2-2y^2\right)\)
\(\Leftrightarrow6x^2y^2-4y^4\)
\(2y^2\cdot2y^2=4y^4\) đúng rồi còn gì, lấy đâu ra x