Giải phương trình: \(8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)^2-4\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)^2=\left(x+4\right)^2\)
Phân tích các đa thức sau thành nhân tử ( đặt biến phụ )
a. \(\left(x^2+x\right)^2-14\left(x^2+x\right)+24\)
b. \(\left(x^2+x\right)^2+4x^2+4x-12\)
c. \(x^4+2x^3+5x^2+4x-12\)
d.\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
e. \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)
f. \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)
Bài 3
a) \(\left(x^2+x\right)^2+4x^2+4x\)
b) \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
1.Phân tích đa thức thành nhân tử bằng phương pháp đặt ẩn phụ:
\(a.\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
\(b.\left(x^2+x+1\right).\left(x^2+x+2\right)-12\)
\(c.\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)
GIÚP MỊ NHA!
Phân tích thành nhân tử
a. \(\left(x^2+8x+7\right)\left(x+3\right)\left(x+5\right)+15\)
b. \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4\)
c. \(\left(x+5\right)\left(x+6\right)\left(x+10\right)\left(x+12\right)-3x^2\)
a) \(x^2.\left(1-x^2\right)-4-4x^2\)
b)\(\left(1+2x\right)\left(1-2x\right)-\left(x+2\right)\left(x-20\right)\)
c)\(x^2+y^2-x^2y^2+xy-x-y\)
Bài 3.
a) \(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
b)\(\left(x^2+x\right)\left(x^2+x+1\right)-6\)
c)\(\left(x^2-4x\right)^2-8\left(x-4x\right)+15\)
Cho \(\left(x-\dfrac{1}{x}\right):\left(x+\dfrac{1}{x}\right)\)\(=\dfrac{1}{2}\). Tính \(\left(x^2-\dfrac{1}{x^2}\right):\left(x^2+\dfrac{1}{x^{2.}}\right)\)
Bài 1: Phân tích đa thức thành nhân tử:
a) \(2x\left(x+1\right)+2\left(x+1\right)\)
b) \(y^2\left(x^2+y\right)-zx^2-zy\)
c) \(4x\left(x-2y\right)+8y\left(2y-x\right)\)
d) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)
e) \(x^2-6xy+9y^2\)
f) \(x^3+6x^2y+12xy^2+8y^3\)
g) \(x^3-64\)
h) \(125x^3+y^6\)
k) \(0,125\left(a+1\right)^3-1\)
t) \(x^2-2xy+y^2-xz+yz\)
q) \(x^2-y^2-x+y\)
p) \(a^3x-ab+b-x\)
đ) \(3x^2\left(a+b+c\right)+36xy\left(a+b+c\right)+108y^2\left(a+b+c\right)\)
l) \(x^2-x-6\)
i) \(x^4+4x^2-5\)
m) \(x^3-19x-30\)
j) \(x^4+x+1\)
y) \(ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\)
o) \(\left(a+b+c\right)^3-a^3-b^3-c^3\)
ê) \(4a^2b^2-\left(a^2+b^2+c^2\right)^2\)
w) \(\left(1+x^2\right)^2-4x\left(1-x^2\right)\)
z) \(\left(x^2-8\right)^2+36\)
u) \(81x^4+4\)
Bài 2 : Tìm x
a)\(\left(2x-1\right)^2-25=0\)
b) \(8x^3-50x=0\)
c) \(\left(x-2\right)\left(x^2+2+7\right)+2\left(x^2-4\right)-5\left(x-2\right)=0\)
d) \(3x\left(x-1\right)+x-1=0\)
e) \(2\left(x+3\right)-x^2-3x\) =0
f) \(4x^2-25-\left(2x-5\right)\left(2x+7\right)=0\)
g) \(x^3+27+\left(x+3\right)\left(x-9\right)=0\)
Giải các phương trình sau:
a,\(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6\)
b,\(4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10\)