xy-4x-4y=25
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xy - 4x - 4y = 25
=> x(y - 4) - 4y + 16 = 25 + 16
=> x(y - 4) - 4(y - 4) = 41
=> (x - 4)(y - 4) = 41
xét bảng :
x-4 | -1 | 1 | -41 | 41 |
y-4 | -41 | 41 | -1 | 1 |
x | 3 | 5 | -37 | 45 |
y | -37 | 45 | 3 | 5 |
5.
\(4x^5y^2+8x^4y^3+4x^3y^4=4x^3y^2(x^2+2xy+y^2)\)
\(=4x^3y^2(x+y)^2\)
9.
\(4x^5y^2+16x^4y^2-6x^3y^2=2x^3y^2(2x^2+4x-3)\)
13.
\(-3x^4y+6x^3y-3x^2y=-3x^2y(x^2-2x+1)=-3x^2y(x-1)^2\)
17.
\(8x^3-8x^2y+2xy^2=2x(4x^2-4xy+y^2)\)
\(=2x[(2x)^2-2.2x.y+y^2]=2x(2x-y)^2\)
21.
\((a^2+4)^2-16a^2b^2=(a^2+4)^2-(4ab)^2\)
\(=(a^2+4-4ab)(a^2+4+4ab)\)
25.
\(100a^2-(a^2+25)^2=(10a)^2-(a^2+25)^2\)
\(=(10a-a^2-25)(10a+a^2+25)\)
\(=-(a^2-10a+25)(a^2+10a+25)=-(a-5)^2(a+5)^2\)
29.
\(25a^2b^2-4x^2+4x-1=25a^2b^2-(4x^2-4x+1)\)
\(=(5ab)^2-(2x-1)^2=(5ab-2x+1)(5ab+2x-1)\)
\(=x\left(x+4\right)+y\left(x+4\right)=\left(x+y\right)\left(x+4\right)\)
\(a.10x\left(x-y\right)-6y\left(y-x\right)\\ =10x\left(x-y\right)+6y\left(x-y\right)\\ =\left(10x-6y\right)\left(x-y\right)\\ =2\left(5x-3y\right)\left(x-y\right)\)
\(b.14x^2y-21xy^2+28x^3y^2\\ =7xy\left(x-y+xy\right)\)
\(c.x^2-4+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2+x-2\right)\\ =2x\left(x-2\right)\)
\(d.\left(x+1\right)^2-25\\ =\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
a) x2 - y2 - 4x + 4y
= (x2 - 4x + 4) - (y2 - 4y + 4)
= (x - 2)2 - (y - 2)2
= (x - 2 - y + 2)(x - 2 + y - 2)
= (x - y)(x + y - 4)
b) (xy + 4)2 - 4(x + y)2
= (xy + 4)2 - [2(x + y)]2
= (xy + 4)2 - (2x + 2y)2
= (xy + 4 - 2x - 2y)(xy + 4 + 2x + 2y)
c) 25 - x2 + 2xy - y2
= 25 - (x2 - 2xy + y2)
= 52 - (x - y)2
=> (5 - x + y)(5 + x - y)
a) \(x^2-y^2-4x+4y=\left(x^2-y^2\right)-\left(4x-4y\right)=\left(x+y\right)\left(x-y\right)-4\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-4\right)\)
b) \(\left(xy+4\right)^2-4\left(x+y\right)^2=\left(xy+4\right)^2-\left(2x+2y\right)^2=\left(xy+4+2x+2y\right)\left(xy+4-2x-2y\right)\)
c) \(25-x^2+2xy-y^2=25-\left(x^2-2xy+y^2\right)=5^2-\left(x-y\right)^2=\left(5+x-y\right)\left(5-x+y\right)\)
a) \(4y^2-4x^2-4y+1\)
\(=\left(4y^2-4y+1\right)-4x^2\)
\(=\left(2y-1\right)^2-\left(2x\right)^2\)
\(=\left(2y-2x-1\right)\left(2y+2x-1\right)\)
xy - 4x - 4y = 25
=> x(y - 4) - 4y + 16 = 25 + 16
=> x(y - 4) - 4(y - 4) = 41
=> (x - 4)(y - 4) = 41
=> tự xét bảng
Ta có : xy - 4x - 4y = 25
=> x(y - 4) - 4y = 25
=> x(y - 4) - 4y + 16 = 25 + 16
=> x(y - 4) - (4y - 16) = 41
=> x(y - 4) - 4(y - 4) = 41
=> (x - 4)(y - 4) = 41
mà 41 = 1.41 = (-1).(- 41)
Lập bảng xét các trường hợp ta có :
Vậy các cặp (x;y) thỏa mãn là : (5;45) ; (45;5) ; (3; - 37) ; (- 37;3)