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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: \(x\left(x+1\right)\left(x+6\right)-x^3=5x\)
\(\Rightarrow\left(x^2+x\right)\left(x+6\right)-x^3=5x\)
\(\Rightarrow x^3+x^2+6x^2+6x-x^3=5x\)
\(\Rightarrow7x^2=-x\)
\(\Rightarrow7x=-1\Rightarrow x=\dfrac{-1}{7}\).
Bài 1:
a) \(3x^2-2x(5+1,5x)+10=3x^2-(10x+3x^2)+10\)
\(=10-10x=10(1-x)\)
b) \(7x(4y-x)+4y(y-7x)-2(2y^2-3,5x)\)
\(=28xy-7x^2+(4y^2-28xy)-(4y^2-7x)\)
\(=-7x^2+7x=7x(1-x)\)
c)
\(\left\{2x-3(x-1)-5[x-4(3-2x)+10]\right\}.(-2x)\)
\(\left\{2x-(3x-3)-5[x-(12-8x)+10]\right\}(-2x)\)
\(=\left\{3-x-5[9x-2]\right\}(-2x)\)
\(=\left\{3-x-45x+10\right\}(-2x)=(13-46x)(-2x)=2x(46x-13)\)
Bài 2:
a) \(3(2x-1)-5(x-3)+6(3x-4)=24\)
\(\Leftrightarrow (6x-3)-(5x-15)+(18x-24)=24\)
\(\Leftrightarrow 19x-12=24\Rightarrow 19x=36\Rightarrow x=\frac{36}{19}\)
b)
\(\Leftrightarrow 2x^2+3(x^2-1)-5x(x+1)=0\)
\(\Leftrightarrow 2x^2+3x^2-3-5x^2-5x=0\)
\(\Leftrightarrow -5x-3=0\Rightarrow x=-\frac{3}{5}\)
\(2x^2+3(x^2-1)=5x(x+1)\)
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) y(x2-y2)(x2+y2)-y(x4-y4)=y[(x2)2-(y2)2] - y(x4-y4)=y(x4-y4)-y(x4-y4)=0
vậy giá trị biểu thức không phụ thuộc vào biến (đpcm)
b) \(\left(\frac{1}{3}+2x\right)\left(4x^2-\frac{2}{3}x+\frac{1}{9}\right)-\left(8x^3-\frac{1}{27}\right)\)
\(=\left[\left(2x\right)^3+\left(\frac{1}{3}\right)^3\right]-\left(8x^3-\frac{1}{27}\right)=8x^3+\frac{1}{27}-8x^3+\frac{1}{27}=\frac{1}{54}\)
vậy giá trị biểu thức không phụ thuộc vào biến (đpcm)
c) (x - 1)^3 - (x - 1)(x^2 + x + 1) - 3(1 - x)x
= (x - 1)(x^2 + x + 1) - (x - 1)(x^2 + x + 1) - 3x(1 - x)
= x^3 - 3x^2 + 3x - 1 - x^3 + 1 - 3x + 3x^2
= 0 (đpcm)
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