(=)x3+9x2+27x+27-9x3+6x2-x+8x3+1=28
(=)15x2+26x=0
(=)x(15x+26)=0
=>\(\left\{{}\begin{matrix}x=0\\x=-\dfrac{26}{15}\end{matrix}\right.\)
B)(=) (x2-1)[(x2-1)2-(x4+x2+ 1)]=0
(=) (x2-1)(x4-2x2+1-x4-x2-1)=0
(=)(x+1)(x-1).(-3x2)=0
=>\(\left\{{}\begin{matrix}x+1=0\\x-1=0\\x=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\x=1\\x=0\end{matrix}\right.\)
Tìm x :
a, \(\left(2x+1\right)^2-3x^2+4=\left(1-x\right).\left(1+x\right)\)
b, \(\left(4x-3\right)\cdot\left(4x+3\right)-2\cdot\left(x+2\right)^2=14x^2\)
c, \(\left(2x-1\right)\cdot\left(x+1\right)-x^2+1=\dfrac{1}{2}\cdot\left(x-1\right)^2\)
Tìm x :
a, \(4x^2-\left(3x+1\right)\cdot\left(2x-1\right)=2\cdot\left(x-3\right)^2\)
b.\(\left(5x-1\right)\cdot\left(x+1\right)-\left(2x-1\right)\cdot\left(2x+1\right)=x\cdot\left(x+1\right)\)
c, \(7x^2-\left(2x-3\right)^2=1+3\cdot\left(x+2\right)^2\)
tìm x biết
a)\(\left(x-2\right)^2-x\left(x+1\right)\left(x-1\right)+6x\left(x-3\right)=0\)
b)\(\left(x-2\right)\left(x^2-2x+4\right)\left(x+2\right)\left(x^2+2x+4\right)-x^6+2x=1\)
c)\(\left(x-3\right)\left(x^2+3x+9\right)+x\left(x+2\right)\left(2-x\right)=1\)
Tìm x:
\(1,\left(3x-5\right)^2-\left(3x+1\right)^2=8\)
2,\(2x.\left(8x-3\right)-\left(4x-3\right)^2=27\)
3,\(\left(2x-3\right)^2-\left(2x+1\right)^2=3\)
4, \(\left(x+5\right)^2-x^2=45\)
5, \(\left(x-3\right)^3-\left(x-3\right).\left(x^2+3x+9\right)+9.\left(x+1\right)^2=18\)
6,\(x.\left(x-4\right).\left(x+4\right)-\left(x-5\right).\left(x^2+5x+25\right)=13\)
Chứng minh biểu thức không phụ thuộc x :
1, \(\left(3x-1\right)^2-2\cdot\left(2x-3\right)\cdot\left(2x+3\right)-\left(x-3\right)^2\)
2, \(\left(3x+2\right)^3-\left(3x-2\right)^3-3\cdot\left(6x-1\right)\cdot\left(6x+1\right)\)
3, \(\left(3x-5\right)^2+3\cdot\left(x+1\right)\cdot\left(x-1\right)-\left(4x-3\right)^2+\left(2x+2\right)\cdot\left(2x+1\right)\)
1) Tìm x biết,
\(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)=11\)
2) Rút gọn các biểu thức
a) \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
b) \(\left(a-b+c\right)^2-\left(b-c\right)^2+2ab-2ac\)
c) \(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)
d) \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
e) \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)
3) Chứng minh rằng các biểu thức sau luôn luôn có giá trị dương với mọi giá trị của biến
a) \(9x^2-6x+2\)
b) \(x^2+x+1\)
c) \(2x^2+2x+1\)
4) Tìm GTNN của các biểu thức
a) A=\(x^2-3x+5\)
b) B=\(\left(2x-1\right)^2+\left(x+2\right)^2\)
GIÚP MK VỚI!!!!!!!!!!
1.Tìm x:
\(\left(x-1\right)^3+\left(2x+1\right)^3+\left(x+2\right)^3=3\left(x-1\right).\left(2x+1\right).\left(x+2\right)\)
2. Cho \(a+b+c=0\) . C/m: \(a^3+b^3+c^3=3abc\)
3. Tìm x:
a, \(\left(x+1\right)^3+\left(2x-3\right)^3+\left(2-3x\right)^3=0\)
b, \(\left(2x+1\right)^3+\left(x+2\right)^3=27\left(x+1\right)^3\)
Chứng minh giá trị biểu thức không phụ thuộc x :
1, \(\left(2x+1\right)^3-\left(2x-1\right)^3-2\cdot\left(4x+3\right)^2+8\cdot\left(x+3\right)^2\)
2,\(\left(2x+1\right)^2\cdot\left(x-1\right)-2\cdot\left(x-2\right)^3+x\cdot\left(3-2x\right)\cdot\left(3+x\right)-\left(3x-3\right)^2\)
Dùng hằng đẳng thức để triển khai và thu gọn:
a) \(x\left(x-1\right).\left(x+1\right)-\left(x+1\right)\left(x^2-x+1\right)\)
b) \(\left(x-1\right)^3-\left(x+2\right).\left(x^2-2x+4\right)+3.\left(x+4\right).\left(x-4\right)\)
c) \(3x^2.\left(x+1\right).\left(x-1\right)+\left(x^2-1\right)^3-\left(x^2-1\right).\left(x^4+x^2+1\right)\)