\(6\left(x+1\right)^2-2\left(x+1\right)^3+2\left(x-1\right)\left(x^2+x+1\right)=1\)
⇔ \(6\left(x^2+2x+1\right)-2\left(x^3+3x^2+3x+1\right)+2\left(x^3-1\right)=1\)
⇔ \(6x^2+12x+6-2x^3-6x^2-6x-2+2x^3-2=1\)
⇔ 6x + 1 = 0
⇔ x = \(\dfrac{-1}{6}\)
KL.........
Bài 1 : dùng hẳng đẳng thức để khai triển và thu gọn
a) \(\left(2x^2+\frac{1}{3}\right)^3\)
b) \(\left(2x^2y-3xy\right)^3\)
c) \(\left(-3xy^4+\frac{1}{2}x^2y^2\right)^3\)
d) \(\left(-\frac{1}{3}ab^2-2a^3b\right)^3\)
e) \(\left(x+1\right)^3-\left(x-1\right)^3-6.\left(x-1\right).\left(x+1\right)\)
f) \(x.\left(x-1\right).\left(x+1\right)-\left(x+1\right).\left(x^2-x+1\right)\)
g) \(\left(x-1\right)^3-\left(x+2\right).\left(x^2-2x+4\right)+3.\left(x-4\right).\left(x+4\right)\)
h) \(3x^2.\left(x+1\right).\left(x-1\right)+\left(x^2-1\right)^3-\left(x^2-1\right).\left(x^4+x^2+1\right)\)
k) \(\left(x^4-3x^2+9\right).\left(x^2+3\right)+\left(3-x^2\right)^3-9x^2.\left(x^2-3\right)\)
l) \(\left(4x+6y\right).\left(4x^2-6xy+9y^2\right)-54y^3\)
Giải phương trình sau:
\(3x\times\left|x+1\right|-2x\times\left|x+2\right|=2\) với x>-1
Chứng minh biểu thức sau ko phụ thuộc vào x:
\(A=x\left(x^2+x+1\right)-x^2\left(x+1\right)-x+5\)
\(B=x\left(2x+1\right)-x^2\left(x+2\right)+x^3-x+3\)
\(C=4\left(6-x\right)+x^2\left(2+3x\right)-x\left(5x-4\right)+3x^2\left(1-x\right)\)
\(D=5\left(3x^{n+1}-y^{n-1}\right)+3\left(x^{n+1}+5y^{n-1}\right)-5\left(3x^{n+1}+2y^{n-1}\right)\)
Chứng minh biểu thức sau không phụ thuộc vào giá trị của biến :
\(A=x.\left(5x-3\right)-x^2.\left(x-1\right)+x.\left(x^2-6x\right)-10+3x+x.\left(x^2+x+1\right)-x^2.\left(x+1\right)-x+5\)
\(B=3.\left(2x-1\right)-5.\left(x-3\right)+6.\left(3x-4\right)-19x+x.\left(3x+12\right)-\left(7x-20\right)+x^2.\left(2x-3\right)-x.\left(2x^2+5\right)\)
giải pt sau
a)\(\left(x-2\right)\left(x-3\right)+2x=\left(x-2\right)^2-2\)
b) \(\left(x-1\right)^2+3x\left(x-1\right)+7=\left(2x-1\right)^2+5\left(x-3\right)\)
c)\(5\left(x^1-2x-1\right)+2\left(3x-2\right)=5\left(x+1\right)^2\)
d)\(\left(x-1\right)\left(x^2+x+1\right)-2x=x\left(x-1\right)\left(x+1\right)\)
Thực hiện phép tính:
\(a,\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}\)
\(b,\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}\)
Cho biểu thức
A=\(\left[\frac{3\left(x+2\right)}{2\left(x^3+x^2+x+1\right)}+\frac{2x^2-x-10}{2\left(x^3-x^2+x-1\right)}\right]:\left[\frac{5}{x^2+1}+\frac{3}{2\left(x+1\right)}-\frac{3}{2\left(x+1\right)}\right]\)
giải pt: \(\dfrac{1}{\left(x-1\right)\left(x-2\right)}+\dfrac{1}{\left(x-3\right)\left(x-2\right)}=\dfrac{1}{\left(x-3\right)\left(x-4\right)}+\dfrac{1}{\left(x-1\right)\left(x-4\right)}\)
A=\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+...+\frac{1}{\left(x+9\right)\left(x+100\right)}\)
