`=(x^2 + 6x +9 ) -(x^2 + 2x-2x-4)`
`=x^2 + 6x +9- x^2 -2x+2x+4`
`= 6x +13`
`=(x^2 + 6x +9 ) -(x^2 + 2x-2x-4)`
`=x^2 + 6x +9- x^2 -2x+2x+4`
`= 6x +13`
\(\left(x-1\right)^3+3\left(x-3\right)^2-\left(x+2\right)\left(x^2-2x+4\right)=\left(x+2\right)^3-\left(x-3\right)\left(x^2+9\right)-6x^2+5\)
Chứng minh rằng biểu thức sau không phụ thuộc vào biến x:
a/A= \(\left(x+4\right)\left(x-4\right)-2x\left(3+x\right)+\left(x+3\right)^2\)
b/B=\(\left(x^2+4\right)\left(x+2\right)\left(x-2\right)-\left(x^2+3\right)\left(x^2-3\right)\)
Tìm \(x\):
\(8\)) \(1-\left(x-6\right)=4\left(2-2x\right)\)
\(9\))\(\left(3x-2\right)\left(x+5\right)=0\)
\(10\))\(\left(x+3\right)\left(x^2+2\right)=0\)
\(11\))\(\left(5x-1\right)\left(x^2-9\right)=0\)
\(12\))\(x\left(x-3\right)+3\left(x-3\right)=0\)
\(13\))\(x\left(x-5\right)-4x+20=0\)
\(14\))\(x^2+4x-5=0\)
Tìm x, biết :
a/ \(\dfrac{1}{3}x\left(x^2-4\right)=0\)
b/ \(x\left(x+5\right)=x+5\)
c/ \(x^3-\dfrac{1}{9}x=0\)
3)\(^2-\left(x+5\right)^2=0\)
e/ \(\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
f/ \(x\left(2x-3\right)-6+4x=0\)
g/ \(2\left(3x-2\right)^2-9x^2+4=0\)
h/ \(x^2\left(x+1\right)+2x\left(x+1\right)=0\)
i/ \(4x^2+9x+5=0\)
Tính:
a) \(\left(x^2-2\right).\left(1-x\right)+\left(x+3\right).\left(x^2-3x+9\right)\)
b) \(\left(2x^4+x^3-3x^2+4x-3\right):\left(x^2-x+1\right)\)
Giải phương trình:
a) \(\dfrac{1}{x-2}+3=\dfrac{x-3}{2-x}\)
b) \(\dfrac{3}{\left(x-1\right)\left(x-2\right)}+\dfrac{2}{\left(x-3\right)\left(x-1\right)}=\dfrac{1}{\left(x-2\right)\left(x-3\right)}\)
c) \(1+\dfrac{1}{x+2}=\dfrac{12}{8+x^3}\)
BT3: Tìm x
\(a,\left(x+2\right)^2-9=0\)
\(b,x^2-2x+1=25\)
\(c,\left(5x+1\right)^2-\left(5x-3\right)\left(5x+3\right)=30\)
\(d,\left(x-1\right)\left(x^2+x+1\right)+x\left(x+2\right)\left(2-x\right)=5\)
Chứng minh giá trị của x ko phụ thuộc vào giá trị của biến\(D=\left(5x2\right)^2-\left(6x+1\right)^2+11\left(x-2\right)\left(x+2\right)-16\left(3-2x\right).\)
\(E=4x\left(x-3\right)-\left(x-5\right)^2-3\left(x+1\right)^2+\left(2x+2\right)^2-\left(4x-5\right)\)
\(V=\left(x^2-3\right)^3+9x^2\left(x^3-3\right)-\left(x^2-3\right)\left(x^4+3x^2+9\right)-20.\)
Rút gọn biểu thức:
a) \(A=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)
b) \(B=3x^2\left(x+1\right)\left(x-1\right)-\left(x^2-1\right)\left(x^4+x^2+1\right)+\left(x^2-1\right)^3\)
c) \(C=\left(x+y\right)\left(x^2-xy+y^2\right)+\left(x-y\right)\left(x^2+xy+y^2\right)-2x^3\)
d) \(D=\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)
Giải các phương trình sau:
\(\left(x-5\right)^2+\left(x+3\right)^2=2\left(x-4\right)\left(x+4\right)-5x+7\) \(\left(x+3\right)\left(x-2\right)-2\left(x+1\right)^2=\left(x-3\right)^2-2x^2+4x\)
\(\left(x+1\right)^3-\left(x+2\right)\left(x-4\right)=\left(x-2\right)\left(x^2+2x+4\right)+2x^2\)
\(\left(x-2\right)^3+\left(x-5\right)\left(x+5\right)=x\left(x^2-5x\right)-7x+3\)
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