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a.\(2x\left(7x^2-5x-1\right)=14x^3-10x^2-2x\)
b.\(-2x^3\left(2x^2-3y+5yz\right)=-4x^5+6x^3y-10x^3yz\)
c.\(\left(2x-y\right)\left(4x^2-2xy+y^2\right)=2x\left(4x^2-2xy+y^2\right)-y\left(4x^2-2xy+y^2\right)\)
\(=8x^2-4x^2y+4xy^2-4x^2y+2xy^2-y^3\)
a.2x(7x2−5x−1)=14x3−10x2−2x
b.−2x3(2x2−3y+5yz)=−4x5+6x3y−10x3yz
c.(2x−y)(4x2−2xy+y2)=2x(4x2−2xy+y2)−y(4x2−2xy+y2)
=8x2−4x2y+4xy2−4x2y+2xy2−y3
\(A=-2x^2+5x-8\)
\(A=-2\left(x^2-\frac{5}{2}\cdot x+4\right)\)
\(A=-2\left(x^2-2\cdot x\cdot\frac{5}{4}+\frac{25}{16}+\frac{39}{16}\right)\)
\(A=-2\left[\left(x-\frac{5}{4}\right)^2+\frac{39}{16}\right]\)
\(A=-2\left(x-\frac{5}{4}\right)^2-\frac{39}{6}\le\frac{-39}{6}\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x=\frac{5}{4}\)
\(B=-x^2-y^2+xy+2x+2y\)
\(2B=-2x^2-2y^2+2xy-4x-4y\)
\(2B=-\left(2x^2+2y^2-2xy+4x+4y\right)\)
\(2B=-\left(x^2-2xy+y^2+x^2+4x+4+y^2+4y+4-8\right)\)
\(2B=-\left[\left(x-y\right)^2+\left(x+2\right)^2+\left(y+2\right)^2-8\right]\)
\(B=-\frac{\left(x-y\right)^2+\left(x+2\right)^2+\left(y+2\right)^2}{2}+4\le4\forall x;y\)
Dấu "=" xảy ra \(\Leftrightarrow x=y=-2\)
\(C=\frac{3}{4x^2-4x+5}=\frac{3}{\left(2x-1\right)^2+4}\le\frac{3}{4}\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x=\frac{1}{2}\)
\(D=\frac{x^2-6x+14}{x^2-6x+12}=\frac{x^2-6x+12+2}{x^2-6x+12}\)
\(=1+\frac{2}{\left(x-3\right)^2+3}\le1+\frac{2}{3}=\frac{5}{3}\)
Dấu "=" xảy ra \(\Leftrightarrow x=3\)
\(4x^2-25+\left(2x+7\right)\left(5-2x\right)\)
\(=\left(2x-5\right)\left(2x+5\right)+\left(2x+7\right)\left(5-2x\right)\)
\(=\left(2x-5\right)\left(2x+5\right)-\left(2x-7\right)\left(2x-5\right)\)
\(=\left(2x-5\right)\left(2x+5-2x+7\right)\)
\(=\left(2x-5\right).12\)
Những câu khác làm tương tự
Bài 2:
\(=\dfrac{x^2\left(x^2+4\right)-2x\left(x^2+4\right)}{x^2+4}=x^2-2x\)
Bài 1:
a: \(=\left(\dfrac{2}{3}:\dfrac{-1}{9}\right)\cdot x^4y^2z^6=-6x^4y^2z^6\)
b: \(=-12x^8-21x^5\)
c: =x^3+8
d: \(=125x^3-75x^2+15x-1\)
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
a) \(\left(6x^3y^2-4x^2y^3-10x^2y^2\right):2xy\)
=\(\left(6x^3y^2:2xy\right)-\left(4x^2y^3:2xy\right)-\left(10x^2y^2:2xy\right)\)
\(=3x^2y-2xy^2-5xy\)
b) \(\dfrac{2y}{x-2}+\dfrac{5y}{x-2}\)
=\(\dfrac{2y+5y}{x-2}\)
=\(\dfrac{7y}{x-2}\)
c)\(\dfrac{xy}{3x-y}+\dfrac{3x^2}{y-3x}\)
\(=\dfrac{xy}{3x-y}-\dfrac{3x^2}{3x-y}\)
=\(\dfrac{x\left(y-3x\right)}{3x-y}\)
=\(\dfrac{-x\left(3x-y\right)}{3x-y}\)
=-x
d)\(\dfrac{x-1}{6x+12}.\dfrac{x+2}{x-1}\)
=\(\dfrac{\left(x-1\right)\left(x+2\right)}{6\left(x+2\right)\left(x-1\right)}\)
=\(\dfrac{1}{6}\)
a) \(\left(6x^2y-\dfrac{1}{2}xy+12y\right)\left(-\dfrac{1}{3}xy\right)=-2x^3y^2+\dfrac{1}{6}x^2y^2-4xy^2\)
b) \(\left(2x+3-y\right)\left(2x-y\right)=4x^2+6x-2xy-2xy-3y+y^2=4x^2+y^2+6x-3y-4xy\)
c) \(3\left(4x+1\right)\left(4x-1\right)-12\left(4x^2+1\right)=3\left(16x^2-1\right)-48x^2-12=48x^2-3-48x^2-12=-15\)
b. (2x + 3 - y)(2x - y)
= 4x2 - 2xy + 6x - 3y - 2xy + y2
= 4x2 - 4xy + 6x - 3y + y2
= \(\left[\left(2x\right)^2-4xy+y^2\right]\) + (6x - 3y)
= (2x - y)2 + 3(2x - y)
= (2x - y + 3)(2x - y)