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Bài 2:
\(A=-2x^2+3x-5\)
\(=-2\left(x^2+\frac{3x}{2}-\frac{5}{2}\right)\)
\(=-2\left(x^2-\frac{3x}{2}+\frac{9}{16}\right)-\frac{31}{8}\)
\(=-2\left(x-\frac{3}{4}\right)^2-\frac{31}{8}\le-\frac{31}{8}\)
Dấu = khi \(-2\left(x-\frac{3}{4}\right)^2=0\Leftrightarrow x-\frac{3}{4}=0\Leftrightarrow x=\frac{3}{4}\)
Vậy \(Max_A=-\frac{31}{8}\Leftrightarrow x=\frac{3}{4}\)
a) = 2x2y2(3y2 - 4y2 + 5y)
= 2x2y2 * ( - y2 +5y)
=2x2y2 * y(5-y)
PTĐTTNT
a)
\(6x^2y^4-8x^2y^2+10x^2y^3\)
\(=x^2y^2\left(6y^2-8+10y\right)\)
b)
\(x^2+y^2-3x-3y+2xy\)
\(=x^2+2xy+y^2-3x-3y\)
\(=\left(x+y\right)^2-3\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y-3\right)\)
c)
\(x^2-25-5+2\sqrt{5}\)
\(=x^2-5^2-5+2\sqrt{5}\)
\(=x^2-5\left(5+1+\sqrt{2}\right)\)
a) x2 - 7xy - 18y2
= x2 + 2xy - 9xy - 18y2
= x(x + 2y) - 9y(x + 2y)
= (x - 9y)(x + 2y)
b) 4x2 + 8x - 5
= 4x2 - 2x + 10x - 5
= 2x(2x - 1) + 5(2x - 1)
= (2x + 5)(2x - 1)
c) 4x4 - 21x2y2 + y4
= (4x4 + 4x2y2 + y4) -25x2y2
= (2x2 + y2) - (5xy)2
= (2x2 + 5xy + y2)(2x2 - 5xy + y2)
= \(2\left(x^2+\frac{5}{2}xy+\frac{y^2}{2}\right)2\left(x^2-\frac{5}{2}xy+\frac{y^2}{2}\right)\)
= \(4\left[\left(x+\frac{5}{4}y\right)^2-\frac{25}{16}y^2+\frac{y^2}{2}\right]\left[\left(x-\frac{5}{4}\right)y^2-\frac{25}{16}y^2+\frac{y^2}{2}\right]\)
\(=4\left(x+\frac{5}{4}y-\frac{\sqrt{17}}{4}y\right)\left(x+\frac{5}{4}y+\frac{\sqrt{17}}{4}y\right)\left(x-\frac{5}{4}y-\frac{\sqrt{17}y}{4}\right)\left(x-\frac{5}{4}y+\frac{\sqrt{17y}}{4}\right)\)
a) 25x2 - y2 + 4y - 4
= (5x)2 - (y - 2)2
= (5x + y - 2)(5x - y + 2)
b) a2 + b2 - x2 - y2 + 2ab - 2xy
= (a2 + 2ab + b2) - (x2 + 2xy + y2)
= (a + b)2 - (x + y)2
= (a + b + x + y)(a + b - x - y)
c) 5x2(x - 1) + 10xy(x - 1) - 5y2(1 - x)
= 5x2(x - 1) + 10xy(x - 1) + 5y2(x - 1)
= (x - 1)(5x2 + 10xy + 5y2)
= 5(x - 1)(x2 + 2xy + y2)
= 5(x -1)(x + y)2
d) x5 - x4y - xy4 + y5
= x4(x - y) - y4(x - y)
= (x - y)(x4 - y4)
= (x - y)(x2 - y2)(x2 + y2) = (x - y)2(x + y)(x2 + y2)
a) \(\left(x+a\right)\left(x+2a\right)\left(x+3a\right)\left(x+4a\right)+a^4\)
\(=\left[\left(x+a\right)\left(x+4a\right)\right]\left[\left(x+2a\right)\left(x+3a\right)\right]+a^4\)
\(=\left(x^2+5ax+4a^2\right)\left(x^2+5ax+6a^2\right)+a^4\)
\(=\left(x^2+5ax+5a^2\right)^2-\left(a^2\right)^2+a^4\)
\(=\left(x^2+5ax+5a^2\right)^2\)
b) \(\left(x^2+y^2+z^2\right)\left(x+y+z\right)^2+\left(xy+yz+zx\right)^2\)
\(=\left(x^2+y^2+z^2\right)\left[x^2+y^2+z^2+2\left(xy+yz+zx\right)\right]+\left(xy+yz+zx\right)^2\)
\(=\left(x^2+y^2+z^2\right)^2+2\left(x^2+y^2+z^2\right)\left(xy+yz+zx\right)+\left(xy+yz+zx\right)^2\)
\(=\left(x^2+y^2+z^2+xy+yz+zx\right)^2\)
x5+x4+x3+x2+x+1
=x3.(x2+x+1)+(x2+x+1)
=(x2+x+1)(x3+1)
=(x2+x+1)(x+1)(x2-x+1)