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Theo bài ra , ta có :
\(A=2\left(x^6-y^6\right)-3\left(x^4+y^4\right)+1\)
\(\Leftrightarrow A=2[\left(x^2\right)^3-\left(y^2\right)^3]-3\left(x^4+y^4\right)+1\)
\(\Leftrightarrow A=2\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)-3\left(x^4+y^4\right)+1\)
\(\Leftrightarrow A=2x^4+2x^2y^2+2y^4-3x^4-3y^4\)(Vì x2 - y2 = 1)
\(\Leftrightarrow A=-x^4+2x^2y^2-y^4+1=-\left(x^4-2x^2y^2+y^4\right)=-\left(\left(x^2-y^2\right)^2\right)=-1+1=0\)Vậy A = 0
Chúc bạn học tốt =))
\(A=\left(x+1\right)^3-\left(x+3\right)^2\left(x+1\right)+4x^2+8\)\(=\left(x+1\right)\left[\left(x+1\right)^2-\left(x+3\right)^2\right]+4x^2+8\)
\(=\left(x+1\right)\left(x+1+x+3\right)\left(x+1-x-3\right)+4x^2+8\)\(=\left(x+1\right)\left(2x+4\right).-2+4x^2+8=-2\left(2x^2+4x+2x+4\right)+4x^2+8=-4x^2-12x-8+4x^2+8=-12x\) Với \(x=\dfrac{-1}{6}\Rightarrow A=\left(-12\right).\left(\dfrac{-1}{6}\right)=2\)
a: \(A=x^3+3x^2+3x+1-\left(x^2+6x+9\right)\left(x+1\right)+4x^2+8\)
\(=x^3+7x^2+3x+9-x^3-x^2-6x^2-6x-9x-9\)
\(=-12x\)
\(=-12\cdot\dfrac{-1}{6}=2\)
b: Sửa đề: \(B=2\left(x^6+y^6\right)-3\left(x^4+y^4\right)\)
\(=2\left[\left(x^2+y^2\right)\left(x^4-x^2y^2+y^4\right)\right]-3\left(x^4+y^4\right)\)
\(=2x^4-2x^2y^2+2y^4-3x^4-3y^4\)
\(=-\left(x^4+2x^2y^2+y^4\right)=-1\)
Câu 1 :
\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)=\left(2x\right)^3+y^3=8x^3+y^3\)Câu 2:
\(A=3\left(2x-3\right)\left(3x+2\right)-2\left(x+4\right)\left(4x-3\right)+9x\left(4-x\right)=0\)\(\Leftrightarrow3\left(6x^2-2x-6\right)-2\left(4x^2+13x-12\right)+36x-9x^2=0\)\(\Leftrightarrow18x^2-6x-18-8x^2-26x+24+36x-9x^2=0\)\(\Leftrightarrow x^2+4x+6=0\)
\(\Leftrightarrow\left(x+2\right)^2=-2\)
Ta có:
\(\left(x+2\right)^2\ge0\forall x\)
Vậy pt vô nghiệm
Vậy:ko......
Câu 3:
\(\left(5x-3\right)\left(7x+2\right)-35x\left(x-1\right)=42\)
\(\Leftrightarrow35x^2+10x-21x-6-35x^2+35x-42=0\)\(\Leftrightarrow14x=48\Leftrightarrow x=\dfrac{7}{24}\)
Câu 4:
\(\left(3x+5\right)\left(2x-1\right)+\left(5-6x\right)\left(x+2\right)=x\)
\(\Leftrightarrow6x^2-3x+10x-5+5x+10-6x^2-12x-x=0\)\(\Leftrightarrow-x=-5\Rightarrow x=5\)
câu 6,
Câu 6: \(\left(10x+9\right)x-\left(5x-1\right)\left(2x+3\right)=8\)
\(\Rightarrow10x^2+9x-\left(10x^2-2x+15x-3\right)=8\)
\(\Rightarrow10x^2+9x-10x^2+2x-15x+3=8\)
\(\Rightarrow-4x+3=8\)
\(\Rightarrow-4x=5\Rightarrow x=\dfrac{-5}{4}\)
Câu 7: \(x\left(x+1\right)\left(x+6\right)-x^3=5x\)
\(\Rightarrow\left(x^2+x\right)\left(x+6\right)-x^3=5x\)
\(\Rightarrow x^3+x^2+6x^2+6x-x^3=5x\)
\(\Rightarrow7x^2=-x\)
\(\Rightarrow7x=-1\Rightarrow x=\dfrac{-1}{7}\).
a, A = (x-1)(x+6) (x+2)(x+3)
= (x^2 + 5x -6 ) (x^2 + 5x + 6)
Đặt t = x^2 +5x
A= (t-6)(t+6)
= t^2 - 36
GTNN của A là -36 khi và ck t= 0
<=> x^2 +5x = 0
<=> x=0 hoặc x=-5
Vậy...
a)
\(\begin{array}{l}A = 0,2\left( {5{\rm{x}} - 1} \right) - \dfrac{1}{2}\left( {\dfrac{2}{3}x + 4} \right) + \dfrac{2}{3}\left( {3 - x} \right)\\A = x - 0,2 - \dfrac{1}{3}x - 2 + 2 - \dfrac{2}{3}x\\ = \left( {x - \dfrac{1}{3}x - \dfrac{2}{3}x} \right) + \left( {\dfrac{{ - 1}}{2} - 2 + 2} \right)\\ = - \dfrac{1}{2}\end{array}\)
Vậy \(A = - \dfrac{1}{2}\) không phụ thuộc vào biến x
b)
\(\begin{array}{l}B = \left( {x - 2y} \right)\left( {{x^2} + 2{\rm{x}}y + 4{y^2}} \right) - \left( {{x^3} - 8{y^3} + 10} \right)\\B = \left[ {x - {{\left( {2y} \right)}^3}} \right] - {x^3} + 8{y^3} - 10\\B = {x^3} - 8{y^3} - {x^3} + 8{y^3} - 10 = - 10\end{array}\)
Vậy B = -10 không phụ thuộc vào biến x, y.
c)
\(\begin{array}{l}C = 4{\left( {x + 1} \right)^2} + {\left( {2{\rm{x}} - 1} \right)^2} - 8\left( {x - 1} \right)\left( {x + 1} \right) - 4{\rm{x}}\\{\rm{C = 4}}\left( {{x^2} + 2{\rm{x}} + 1} \right) + \left( {4{{\rm{x}}^2} - 4{\rm{x}} + 1} \right) - 8\left( {{x^2} - 1} \right) - 4{\rm{x}}\\C = 4{{\rm{x}}^2} + 8{\rm{x}} + 4 + 4{{\rm{x}}^2} - 4{\rm{x}} + 1 - 8{{\rm{x}}^2} + 8 - 4{\rm{x}}\\C = \left( {4{{\rm{x}}^2} + 4{{\rm{x}}^2} - 8{{\rm{x}}^2}} \right) + \left( {8{\rm{x}} - 4{\rm{x}} - 4{\rm{x}}} \right) + \left( {4 + 1 + 8} \right)\\C = 13\end{array}\)
Vậy C = 13 không phụ thuộc vào biến x
A = 2(x^2 - y^2).(x^4 + x^2y^2 + y^4) - 3x^4 - 3y^4 +1
A = 2x^4 + 2.x^2y^2 + 2y^4 - 3x^4 - 3y^4 +1
A = -x^4 + 2.x^2y^2 -y^4 +1
A = - (x^2 - y^2) +1
A = -1 + 1 =0