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1:
a) \(x^3+2x^2+x=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\)
b) \(25-x^2+4xy-4y^2=25-\left(x-2y\right)^2=\left(5-x+2y\right)\left(5+x-2y\right)\)
2
\(-2x^2-4x+6=0\)
\(\Leftrightarrow-2\left(x^2+2x-3\right)=0\)
\(\Leftrightarrow x^2-x+3x-3=0\)
\(\Leftrightarrow x\left(x-1\right)+3\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-1=0\\x+3=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\x=-3\end{array}\right.\)
1,
a) x( x2 + 2x +1) = x(x+1)2
b)25 - (x-2y)2 = (5-x+2y)(5+x-2y)
2,
(x-1)(x+3)=0
<=>x=1 hoặc x=-3
\(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\begin{array}{l} a){\left( {ab - 1} \right)^2} + {\left( {a + b} \right)^2}\\ = {a^2}{b^2} - 2ab + 1 + {a^2} + 2ab + {b^2}\\ = {a^2}{b^2} + 1 + {a^2} + {b^2}\\ = {a^2}\left( {{b^2} + 1} \right) + \left( {{b^2} + 1} \right)\\ = \left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)\\ c){x^3} - 4{x^2} + 12x - 27\\ = {x^3} - 27 + \left( { - 4{x^2} + 12x} \right)\\ = \left( {x - 3} \right)\left( {{x^2} + 3x + 9} \right) - 4x\left( {x - 3} \right)\\ = \left( {x - 3} \right)\left( {{x^2} + 3x + 9 - 4x} \right)\\ = \left( {x - 3} \right)\left( {{x^2} - x + 9} \right)\\ b){x^3} + 2{x^2} + 2x + 1\\ = {x^3} + 2{x^2} + x + x + 1\\ = x\left( {{x^2} + 2x + 1} \right) + \left( {x + 1} \right)\\ = x{\left( {x + 1} \right)^2} + \left( {x + 1} \right)\\ = \left( {x + 1} \right)\left( {x\left( {x + 1} \right) + 1} \right)\\ = \left( {x + 1} \right)\left( {{x^2} + x + 1} \right)\\ d){x^4} - 2{x^3} + 2x - 1\\ = {x^4} - 2{x^3} + {x^2} - {x^2} + 2x - 1\\ = {x^2}\left( {{x^2} - 2x + 1} \right) - \left( {{x^2} - 2x + 1} \right)\\ = \left( {{x^2} - 2x + 1} \right)\left( {{x^2} - 1} \right)\\ = {\left( {x - 1} \right)^2}\left( {x - 1} \right)\left( {x + 1} \right)\\ = {\left( {x - 1} \right)^3}\left( {x + 1} \right)\\ e){x^4} + 2{x^3} + 2{x^2} + 2x + 1\\ = {x^4} + 2{x^3} + {x^2} + {x^2} + 2x + 1\\ = {x^2}\left( {{x^2} + 2x + 1} \right) + \left( {{x^2} + 2x + 1} \right)\\ = \left( {{x^2} + 2x + 1} \right)\left( {{x^2} + 1} \right)\\ = {\left( {x + 1} \right)^2}\left( {{x^2} + 1} \right) \end{array} |
nhiều quá bạn ạ
hay bạn tìm hiểu cách thức chung làm dạng bài tìm GTNN chứ như thế này thì làm lâu lắm
mik chỉ tìm hiểu đc đến câu I còn lại mik k hiểu lắm, bn có lm đc k, giúp mik vs
Bài 1:
a) \(x.\left(x^2-2xy+1\right)=x^3-2x^2y+x\)
b) \(\left(2x-3\right).\left(x+2\right)=2x^2+4x-3x-6=2x^2-x-6\)
Bài 2:
a) \(x^3-2x^2+x=x.\left(x^2-2x+1\right)=x.\left(x-1\right)^2\)
b) \(x^2-xy+2x-2y=\left(x^2-xy\right)+\left(2x-2y\right)=x.\left(x-y\right)+2.\left(x-y\right)=\left(x-y\right).\left(x+2\right)\)
c) Đề sai.
Tạm thời phân tích như sau:
i) x4 - 2x3 + 2x - 1
= (x4 - 1) - (2x3 - 2x)
= (x2 + 1).(x2 -1) - 2x.(x2 - 1)
= (x2 - 1).(x2 - 2x + 1)
j) a6 - a4 + 2a3 + 2a2
= (a3 + a2).(a3 - a2) + 2.(a3 + a2)
= (a3 + a2).(a3 - a2 +2)
k) x4 - x3 + 2x2 + x + 1 (tạm thời giải thế này)
= x3.(x - 1) + (2x + 3 - \(\frac{4}{x-1}\)).(x -1)
= (x - 1).(x3 + 2x + 3 - \(\frac{4}{x-1}\))
Nếu đề là:
x4 + x3 + 2x2 + x + 1
= x4 + x2 + x3 + x + x2 + 1
= x2.(x2 + 1) + x.(x2 + 1) + x2 + 1
= (x2 + 1).(x2 + x + 1)
m) x2y + xy2 + x2z + y2z + 2xyz
= xy.(x + y) + z.(x2 + 2xy + y2)
= xy.(x + y) + z.(x + y).(x + y)
= (x + y).(xy + xz + yz)
n) x5 + x4 + x3 + x2 + x + 1
= x4.(x + 1) + x2.(x + 1) + x + 1
= (x + 1).(x4 + x2 + 1)
\(x^4-2x^3+2x-1\)
\(=\left(x^4-1\right)-2x\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2-2x+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-1\right)^2\)
\(=\left(x-1\right)^3\left(x+1\right)\)
\(a,9x-x^3=x\left(9-x^2\right)=x\left(3-x\right)\left(3+x\right)\)
\(b,\left(2xy+1\right)^2-\left(2x+y\right)^2\)
\(=\left(2xy+1-2x-y\right)\left(2xy+1+2x+y\right)\)
\(c,x^3+2x^2-6x-27\)
\(=x^3+5x^2+9x-3x^2-15x-27\)
\(=\left(x^3-3x^2\right)+\left(5x^2-15x\right)+\left(9x-27\right)\)
\(=x^2\left(x-3\right)+5x\left(x-3\right)+9\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+5x+9\right)\)
\(d,\left(x+y\right)^2-\left(x+y\right)\left(x-y\right)\)
\(=\left(x+y\right)\left(x+y-x+y\right)\)
\(=2y\left(x+y\right)\)
\(e,x-2x^2-4y^2-4y\)
Câu này ko phân tích đc nhé bn
Bn kiểm tra lại đề bài
\(g,x^3-x^2-5x+125\)
\(=x^3-6x^2+25x+5x^2-30x+125\)
\(=\left(x^3+5x^2\right)-\left(6x^2+30x\right)+\left(25x+125\right)\)
\(=x^2\left(x+5\right)-6x\left(x+5\right)+25\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
a, 5x2 - 45x = 5x(x - 9)
b, 3x3y - 6x2y - 3xy3 - 6axy2 - 3a2xy + 3xy
= 3xy(x2 - 2x - y2 - 2ay - a2 + 1)
= 3xy[ (x2 - 2x + 1) - (a2 + 2ay + y2) ]
= 3xy[ (x - 1)2 - (a + y)2 ]
= 3xy(x - 1 + a + y)(x - 1 - a - y)
f, 3xy2 - 12xy + 12x
= 3x(y2 - 4y + 4)
= 3x(y - 2)2
g, 2x2 - 8x + 8
= 2(x2 - 4x + 4)
= 2(x - 2)2
h, 5x3 + 10x2y + 5xy2
= 5x( x2 + 2xy + y2 )
= 5x(x + y)2
k, x2 + 4x - 2xy - 4y + y2
= (x2 - 2xy + y2) + (4x - 4y)
= (x - y)2 + 4(x - y)
= (x - y)(x - y + 4)
i, x3 + ax2 - 4a - 4x
= (x3 - 4x) + (ax2 - 4a)
= x(x2 - 4) + a(x2 - 4)
= (x + a)(x2 - 4)
= (x + a)(x + 2)(x - 2)
Chúc bạn học tốt !
h: \(=\left(x+3\right)\cdot\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)