N=x2/(x+y)(1-y)-y2/(x+y)(1+x)-x2y2/(1+x)(1-y)
1). x2y2(y-x)+y2z2(z-y)-z2x2(z-x)
2)xyz-(xy+yz+xz)+(x+y+z)-1
3)yz(y+z)+xz(z-x)-xy(x+y)
4)2a2b+4ab2-a2c+ac2-4b2c+2bc2-4abc
5)y(x-2z)2+8xyz+x(y-2z)2-2z(x+y)2
6)8x3(y+z)-y3(z+2x)-z3(2x-y)
7) (x2+y2)3+(z2-x2)3-(y2+z2)3
1). x2y2(y-x)+y2z2(z-y)-z2x2(z-x)
2)xyz-(xy+yz+xz)+(x+y+z)-1
3)yz(y+z)+xz(z-x)-xy(x+y)
4)2a2b+4ab2-a2c+ac2-4b2c+2bc2-4abc
5)y(x-2z)2+8xyz+x(y-2z)2-2z(x+y)2
6)8x3(y+z)-y3(z+2x)-z3(2x-y)
7) (x2+y2)3+(z2-x2)3-(y2+z2)3
bn gõ bài trong công thức trực quan ik, khó nhìn lắm, ko làm đc
1) \(x^2y^2\left(y-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=x^2y^3-x^3y^2+y^2z^3-y^3z^2-z^2x^2\left(z-x\right)\)
\(=\left(y^2z^3-x^3y^2\right)-\left(y^3z^2-x^2y^3\right)-z^2x^2\left(z-x\right)\)
\(=y^2\left(z^3-x^3\right)-y^3\left(z^2-x^2\right)-z^2x^2\left(z-x\right)\)
\(=y^2\left(z-x\right)\left(z^2+zx+x^2\right)-y^3\left(z-x\right)\left(z+x\right)-z^2x^2\left(z-x\right)\)
\(=\left(z-x\right)\left[y^2\left(z^2+zx+x^2\right)-y^3\left(z+x\right)-z^2x^2\right]\)
\(=\left(z-x\right)\left[\left(y^2z^2+xy^2z+x^2y^2\right)-\left(y^3z+xy^3\right)-z^2x^2\right]\)
\(=\left(z-x\right)\left(y^2z^2+xy^2z+x^2y^2-y^3z-xy^3-z^2x^2\right)\)
\(=\left(z-x\right)\left[\left(y^2z^2-y^3z\right)-\left(x^2z^2-x^2y^2\right)+\left(xy^2z-xy^3\right)\right]\)
\(=\left(z-x\right)\left[y^2z\left(z-y\right)-x^2\left(z^2-y^2\right)+xy^2\left(z-y\right)\right]\)
\(=\left(z-x\right)\left[y^2z\left(z-y\right)-x^2\left(z-y\right)\left(z+y\right)+xy^2\left(z-y\right)\right]\)
\(=\left(z-x\right)\left(z-y\right)\left[y^2z-x^2\left(z+y\right)+xy^2\right]\)
\(=\left(z-x\right)\left(z-y\right)\left(y^2z-x^2z-x^2y+xy^2\right)\)
\(=\left(z-x\right)\left(z-y\right)\left[\left(y^2z-x^2z\right)-\left(x^2y-xy^2\right)\right]\)
\(=\left(z-x\right)\left(z-y\right)\left[z\left(y^2-x^2\right)-xy\left(x-y\right)\right]\)
\(=\left(z-x\right)\left(z-y\right)\left[z\left(y-x\right)\left(y+x\right)+xy\left(y-x\right)\right]\)
\(=\left(z-x\right)\left(z-y\right)\left(y-x\right)\left[z\left(y+x\right)+xy\right]\)
\(=\left(z-x\right)\left(z-y\right)\left(y-x\right)\left(yz+xz+xy\right)\)
2) \(xyz-\left(xy+yz+xz\right)+\left(x+y+z\right)-1\)
\(=xyz-xy-yz-xz+x+y+z-1\)
\(=\left(xyz-xy\right)-\left(yz-y\right)-\left(xz-x\right)+\left(z-1\right)\)
\(=xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+\left(z-1\right)\)
\(=\left(z-1\right)\left(xy-y-x+1\right)\)
\(=\left(z-1\right)\left[\left(xy-y\right)-\left(x-1\right)\right]\)
\(=\left(z-1\right)\left[y\left(x-1\right)-\left(x-1\right)\right]\)
\(=\left(z-1\right)\left(x-1\right)\left(y-1\right)\)
Gỉa sử (x;y) là hai số thỏa mãn x 2 y 2 - 1 = 5 , x 2 y 2 + 2 = 125 thì giá trị của x 2 + y 2 bằng
A. 26
B. 30
C. 20
D. 25
Cho hai số dương x, y thỏa mãn: x + y = 2
CMR: x2y2(x2 + y2) ≤ 2
Với x, y là hai số dương, dễ dàng chứng minh x + y 2,
do x + y = 2 => 0 < xy ≤ 1 (1)
Ta lại có: 2xy( x2 + y2) ≤
=> 0 < 2xy(x2 + y2) ≤ (x+y)4/4 = 4
=> 0 < xy( x2 + y2) ≤ 2 (2)
Nhân (1) với (2) theo vế ta có: x2y2 ( x2 + y2) ≤ 2 (đpcm)
Dấu “=” xảy ra khi x = y = 1
bài 1: thực hiện phép tính
a, (5x-2y).(x2-xy+1)
b, (x-1).(x+1).(x+2)
c, 1/2.x2y2.(2x+y).(2x-y)
a) Ta có: \(\left(5x-2y\right)\left(x^2-xy+1\right)\)
\(=5x^3-5x^2y+5x-2x^2y+2xy^2-2y\)
\(=5x^3-7x^2y+2xy^2+5x-2y\)
b) Ta có: \(\left(x-1\right)\left(x+1\right)\left(x+2\right)\)
\(=\left(x^2-1\right)\left(x+2\right)\)
\(=x^3+2x^2-x-2\)
c) Ta có: \(\dfrac{1}{2}x^2y^2\cdot\left(2x+y\right)\left(2x-y\right)\)
\(=\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)\)
\(=2x^4y^2-\dfrac{1}{2}x^2y^4\)
a) 3x-3y+x2-y2
b) (2xy+1)^2-(2x+y)^2
c)(x2+y2-5)^2-4(x2y2+4xy+4) d) (x2+y2-z2)^2-4x2y2
e) 9x2 +90
x+225-(x-7)^2
bn viết rõ đề đi bn
Vd:x2 là 2.x hay x\(^2\)
Có nhiều chỗ vậy lắm bn ạ,bn viết lại đề đi rồi tụi mk giúp cho.
a) \(3x-3y+x^2-y^2\)
\(=3\left(x-y\right)+\left(x+y\right)\left(x-y\right)\)
\(=\left(3+x+y\right)\left(x-y\right)\)
b) \(\left(2xy+1\right)^2-\left(2x+y\right)^2\)
\(=\left[\left(2xy+1\right)-\left(2x+y\right)\right]\left[\left(2xy+1\right)+\left(2x+y\right)\right]\)
\(=\left(2xy+1-2x-y\right)\left(2xy+1+2x+y\right)\)
\(=\left(y+1\right)\left(2x+1\right)\left(y-1\right)\left(2x-1\right)\)
c) \(\left(x^2+y^2-5\right)^2-4\left(x^2y^2+4xy+4\right)\)
↓
\(=\left(x^2-y^2-2y-1\right)\left(x^2-2xy+y^2-9\right)\)
\(=\left[x^2-\left(y^2+2y+1\right)\right]\left(x^2-2xy+y^2-9\right)\)
\(=\left[x^2-\left(y+1\right)^2\right]\left[\left(x-y\right)^2-3^2\right]\)
\(=\left[x^2-\left(-y-1\right)^2\right]\left(x-y+3\right)\left(x-y-3\right)\)
\(=\left(x+y+1\right)\left(x-y-1\right)\left(x-y+3\right)\left(x-y-3\right)\)
d) \(\left(x^2+y^2-z^2\right)^2-4x^2y^2\)
\(=\left(x^2+y^2-z^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2+y^2-z^2-2xy\right)\left(x^2+y^2-z^2+2xy\right)\)
\(=\left[\left(x-y\right)^2-z^2\right]\left[\left(x+y\right)^2-z^2\right]\)
\(=\left(x-y-z\right)\left(x-y+z\right)\left(x+y-z\right)\left(x+y+z\right)\)
e)
- \(9x^2+90=9\left(x+10\right)\)
- \(x+225-\left(x-7\right)^2\)
\(=x+225-\left(x^2-14x+49\right)\)
\(=x+225-x^2+14x-49\)
\(=-x^2+15x+176\)
\(=-\left(x^2-15x-176\right)\)
Tính giá trị biểu thức:
a) M = t(10 - 4t) - t 2 (2t - 5) – 2t + 5 tại t = 5 2 ;
b) N = x 2 (y - 1) - 5x(1 - y) tại x = -20 và y = 1001;
c) P = y 2 ( x 2 + y - 1) - m x 2 - my+m tại x = 9 và y = -80;
d) Q = x ( x - y ) 2 -y ( x - y ) 2 + x y 2 - x 2 y tại x - y = 7 và xy = 9.
a) Kết quả M = 0. Chú ý: nhân tử chung là 2f - 5 = 0.
b) Kết quả N = 300000.
c) Kết quả p = 0. Chú ý: nhân tử x 2 + y -1 = 0.
d) Kết quả Q = 280. Chú ý: Q = (x - y)[ ( x - y ) 2 - xy].
cho (P): y = -x^2 và đường thẳng (d): y=2x+m-1
tìm m để (d) cắt (P) tại 2 điểm phân biệt A(x1;x2),B(x2;y2) mà x1y1 -x2y2 -x1x2 = 4
Trả lời:
Phương trình hoành độ giao điểm (P) và (d) ta có:
\(-x^2=2x+m-1\)
\(\Leftrightarrow x^2+2x+m-1=0\)(1)
Ta có: \(\Delta=2^2-4.1.\left(m-1\right)\)
\(=4-4m+4\)
\(=8-4m\)
Để phương trình (1) có 2 nghiệm phân biệt \(\Leftrightarrow\Delta>0\)
\(\Leftrightarrow8-4m>0\)
\(\Leftrightarrow4m< 8\)
\(\Leftrightarrow m< 2\)
\(\Rightarrow\)Phương trình (1) có 2 nghiệm phân biệt
\(\Rightarrow\)(d) cắt (P) tại 2 diểm phân biệt \(A\left(x_1,y_1\right);B\left(x_2,y_2\right)\)
Áp dụng Vi-ét \(\hept{\begin{cases}x_1+x_2=-2\left(1\right)\\x_1.x_2=m-1\left(2\right)\end{cases}}\)
Ta có \(y_1=-x_1^2\); \(y_2=-x_2^2\)
Theo đề bài:
\(x_1.y_1-x_2.y_2-x_1.x_2=4\)
\(\Leftrightarrow x_1.\left(-x_1^2\right)-x_2.\left(-x_2^2\right)-x_1.x_2=4\)
\(\Leftrightarrow-x_1^3+x_2^3-x_1.x_2=4\)
\(\Leftrightarrow-\left(x_1^3-x_2^3\right)-\left(m-1\right)=4\)
\(\Leftrightarrow-\left(x_1-x_2\right).\left(x_1^2+x_1.x_2+x_2^2\right)-\left(m-1\right)=4\)
\(\Leftrightarrow-\left(x_1-x_2\right)\left[\left(x_1+x_2\right)^2-2x_1.x_2+x_1.x_2\right]-\left(m-1\right)=4\)
\(\Leftrightarrow-\left(x_1-x_2\right).\left[\left(x_1+x_2\right)^2-x_1.x_2\right]-\left(m-1\right)=4\)
\(\Leftrightarrow-\left(x_1-x_2\right).\left[\left(-2\right)^2-m+1\right]-\left(m-1\right)=4\)
\(\Leftrightarrow-\left(x_1-x_2\right).\left(4-m+1\right)=4+m-1\)
\(\Leftrightarrow-\left(x_1-x_2\right).\left(3-m\right)=m+3\)
\(\Leftrightarrow-\left(x_1-x_2\right)=\frac{m+3}{3-m}\)
\(\Leftrightarrow x_1-x_2=\frac{m+3}{m-3}\)(3)
Từ (1) (3) ta có: \(\hept{\begin{cases}x_1+x_2=-2\\x_1-x_2=\frac{m+3}{m-3}\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x_1=-2+\frac{m+3}{m-3}=\frac{9-m}{m-3}=-\left(m+3\right)\\x_1+x_2=-2\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x_1=\frac{-\left(m+3\right)}{2}\\x_2=\frac{m-1}{2}\end{cases}}\)
Thay x1, x2 vào (2) ta có
\(x_1.x_2=m-1\)
\(\Leftrightarrow\frac{-\left(m+3\right)}{2}.\frac{m-1}{2}=m-1\)
\(\Leftrightarrow\frac{-\left(m+3\right)}{2}=2\)
\(\Leftrightarrow-\left(m+3\right)=4\)
\(\Leftrightarrow m+3=-4\)
\(\Leftrightarrow m=-7\)(TM)
Vậy \(m=-7\) thì thỏa mãn bài toán
Bài 2 Phân tích đa thức sau thành nhân tử
a. x4 + 2x3 − 4x − 4
b. x2(1 − x2) − 4 − 4x2
c. x2 + y2 − x2y2 + xy − x − y
d* a3 + b3 + c3 − 3abc
a) \(x^4+2x^3-4x-4=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
a) Ta có: \(x^4+2x^3-4x-4\)
\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)
\(=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\cdot\left(x^2+2x+2\right)\)
d) Ta có: \(a^3+b^3+c^3-3abc\)
\(=\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\)
\(=\left(a+b+c\right)\left[\left(a+b\right)^2-c\left(a+b\right)+c^2\right]-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)\)
\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-ac-bc\right)\)
1.
a.(-xy)(-2x2y+3xy-7x)
b.(1/6x2y2)(-0,3x2y-0,4xy+1)
c.(x+y)(x2+2xy+y2)
d.(x-y)(x2-2xy+y2)
2.
a.(x-y)(x2+xy+y2)
b.(x+y)(x2-xy+y2)
c.(4x-1)(6y+1)-3x(8y+4/3)
1.
\(a,\left(-xy\right)\left(-2x^2y+3xy-7x\right)\)
\(=2x^3y^2-3x^2y^2+7x^2y\)
\(b,\left(\dfrac{1}{6}x^2y^2\right)\left(-0,3x^2y-0,4xy+1\right)\)
\(=-\dfrac{1}{20}x^4y^3-\dfrac{1}{15}x^3y^3+\dfrac{1}{6}x^2y^2\)
\(c,\left(x+y\right)\left(x^2+2xy+y^2\right)\)
\(=\left(x+y\right)^3\)
\(=x^3+3x^2y+3xy^2+y^3\)
\(d,\left(x-y\right)\left(x^2-2xy+y^2\right)\)
\(=\left(x-y\right)^3\)
\(=x^3-3x^2y+3xy^2-y^3\)
2.
\(a,\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=x^3-y^3\)
\(b,\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=x^3+y^3\)
\(c,\left(4x-1\right)\left(6y+1\right)-3x\left(8y+\dfrac{4}{3}\right)\)
\(=24xy+4x-6y-1-24xy-4x\)
\(=\left(24xy-24xy\right)+\left(4x-4x\right)-6y-1\)
\(=-6y-1\)
#Toru