(*)\(\left(x-2\right)^3-x^2\left(x-6\right)=4\)
\(\Leftrightarrow x^3-6x^2+12x-8-x^3+6x^2=4\)
\(\Leftrightarrow12x=12\)
\(\Rightarrow x=1\)
(*)\(\left(x+1\right)^3-x\left(x-2\right)^2+x-1=0\)
\(\Leftrightarrow x^3+3x^2+3x+1-x\left(x^2-2x+4\right)+x-1=0\)
\(\Leftrightarrow x^3+3x^2+4x-x^3+2x^2-4x=0\)
\(\Leftrightarrow5x^2=0\)
\(\Leftrightarrow x^2=0\)
\(\Rightarrow x=0\)
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 các phương trình sau:
a) \(x^2+\dfrac{2x}{x-1}=8\)
b) \(\dfrac{x^2+2x+1}{x^2+2x+2}+\dfrac{x^2+2x+2}{x^2+2x+3}=\dfrac{7}{6}\)
c) \(\dfrac{x+4}{x-1}+\dfrac{x-4}{x+1}=\dfrac{x+8}{x-2}+\dfrac{x-8}{x+2}+6\)
d) \(\left(x^2+6x+8\right)\left(x^2+8x+15\right)=24\)
e) \(\left(x^2+x-2\right)\left(x^2+9x+18\right)=28\)
f) \(3\left(-x^2+2x+3\right)^4-26x^2\left(-x^2+2x+3\right)^2-9x^4=0\)
g) \(x^4+6x^3+11x^2+6x+1=0\)
h) \(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2=0\)
i) \(\left(x+2\right)^4+\left(x+8\right)^4=272\)
Tìm x,biết:
a/\(x+5x^2=0\Leftrightarrow......\)
b/\(x+1=\left(x+1\right)^2\Leftrightarrow..........\)
c/\(x^3+x=0\Leftrightarrow.......\)
d/\(5x\left(x-2\right)-\left(2-x\right)=0\)
e/\(x\left(2x-1\right)+\frac{1}{3}-\frac{2}{3}x=0\Leftrightarrow........\)
g/\(x\left(x-4\right)+\left(x-4\right)^2=0\Leftrightarrow.....\)
h/\(x^2-3x=0\Leftrightarrow.....\)
i/\(4x\left(x+1\right)=8\left(x+1\right)\Leftrightarrow.....\)
tìm x biết
a)5(x+3)-2x(x+3)=0
b)6x\(\left(x^2-2\right)-\left(2-x^2\right)=0\)
c)\(\left(x+1\right)^2-\left(x+1\right)\left(x-2\right)=0\)
d)\(4x\left(x-2017\right)-x+2017=0\)
e)\(\left(x+4\right)^2-16=0\)
f)\(12x-x^2-36=0\)
Bài 2: tìm x, biết:
a,\(\left(2x-1\right)^2_{ }-19=45\)
b,\(\left(x-3\right)^2-x\left(x-7\right)=12\)
c,\(x^2-4+3x\left(x-2\right)=0\)
d,\(x^2-9=3\left(x-3\right)\)
e,\(3\left(3x^2+1\right)=6-2\left(3x+2\right)\)
h,\(2x\left(x+3\right)-4\left(x+3\right)=0\)
SAVE ME!!!THANK YOU
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 phương trình
1) \(2\left|x-3\right|+\left|5x-1\right|=0\)
2) \(2\left|x\right|-\left|x+1\right|=2\)
3) \(\left|x\right|-2\left|x-2\right|+3\left|x-3\right|=4\)
4) \(\left|x-4\right|-x=2a\) ( a là hằng số)
Chứng minh biểu thức sau ko phụ thuộc vào x:
\(A=x\left(x^2+x+1\right)-x^2\left(x+1\right)-x+5\)
\(B=x\left(2x+1\right)-x^2\left(x+2\right)+x^3-x+3\)
\(C=4\left(6-x\right)+x^2\left(2+3x\right)-x\left(5x-4\right)+3x^2\left(1-x\right)\)
\(D=5\left(3x^{n+1}-y^{n-1}\right)+3\left(x^{n+1}+5y^{n-1}\right)-5\left(3x^{n+1}+2y^{n-1}\right)\)
Bài 1: Rút gọn biểu thức
a. \(\left(x-3\right)\left(x+7\right)-\left(x+5\right)\left(x-1\right)\)
b. \(x^2\left(x-4\right)\left(x+4\right)-\left(x^2+1\right)\left(x^2-1\right)\)
Bài 2: Tìm x
a. \(x^2-25-\left(x+5\right)=0\)
b. \(3x\left(x-2\right)-x+2=0\)
c. \(x\left(x-4\right)-2x+8=0\)
