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\(4x^2-5\left(x-1\right)=-21x-2\)
\(\Leftrightarrow4x^2-5x+5+21x+2=0\)
\(\Leftrightarrow4x^2+16x+7=0\)
\(\Leftrightarrow\left(4x^2+16x+16\right)-9=0\)
\(\Leftrightarrow\left(2x+4\right)^2=9\)
\(\Leftrightarrow\left(2x+4\right)^2=3^2=\left(-3\right)^2\)
TH1 : \(2x+4=3\Rightarrow x=-\frac{1}{2}\)
TH2: \(2x+4=-3\Rightarrow x=-\frac{7}{2}\)
Vậy..............................................................
=.= hok tốt!!
\(4x^2-5x+5=-21x-2\)
\(\Rightarrow4x^2+16x=-7\)
\(\Rightarrow4x\left(x+4\right)=-7\)
Lập bảng
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\(4x^4-21x^2+1\)
\(=\left(2x^2\right)^2+2.2x^2+1-25x^2\)
\(=\left(2x^2+1\right)^2-\left(5x\right)^2\)
\(=\left(2x^2+1-5x\right)\left(2x^2+1+5x\right)\)
\(4x^4-21x^2+1=\left(2x^2-\frac{21}{4}\right)^2-\frac{425}{16}.\)
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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)
= \(2\left(x^2+\frac{5}{2}xy+\frac{y^2}{2}\right)2\left(x^2-\frac{5}{2}xy+\frac{y^2}{2}\right)\)
= \(4\left[\left(x+\frac{5}{4}y\right)^2-\frac{25}{16}y^2+\frac{y^2}{2}\right]\left[\left(x-\frac{5}{4}\right)y^2-\frac{25}{16}y^2+\frac{y^2}{2}\right]\)
\(=4\left(x+\frac{5}{4}y-\frac{\sqrt{17}}{4}y\right)\left(x+\frac{5}{4}y+\frac{\sqrt{17}}{4}y\right)\left(x-\frac{5}{4}y-\frac{\sqrt{17}y}{4}\right)\left(x-\frac{5}{4}y+\frac{\sqrt{17y}}{4}\right)\)
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a) 4x2 - 2x + 3 - 4x.(x - 5) = 7x - 3
--> 4x2 - 2x + 3 - 4x2 + 20x = 7x - 3
--> 4x2 - 2x - 4x2 + 20x - 7x = -3 - 3
--> 11x = -6
--> x = \(\frac{-6}{11}\)
b) -3x.(x - 5) + 5.(x - 1) + 3x2 = 4x
--> -3x2 + 15x + 5x - 5 + 3x2 = 4x
--> -3x2 + 15x + 5x + 3x2 - 4x = 5
--> 16x = 5
--> x = \(\frac{5}{16}\)
c) 7x.(x - 2) - 5.(x - 1) = 21x2 - 14x2 + 3
--> 7x2 - 14x - 5x + 5 = 7x2 + 3
--> 7x2 - 14x - 5x - 7x2 = -5 + 3
--> -19x = -2
--> x = \(\frac{2}{19}\)
d) 3.(5x - 1) - x.(x - 2) + x2 - 13x = 7
--> 15x - 3 - x2 + 2x + x2 - 13x = 7
--> 15x - x2 + 2x + x2 - 13x = 3 + 7
--> 4x = 10
--> x = \(\frac{5}{2}\)
e) \(\frac{1}{5}\)x.(10x - 15) - 2x.(x - 5) = 12
--> 2x2 - 3x - 2x2 + 10x = 12
--> 7x = 12
--> x = \(\frac{12}{7}\)
~ Học tốt ~
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a) 4x2 - 2x + 3 - 4x(x - 5) = 7x - 3
=> 4x2 - 2x + 3 - 4x2 + 20x = 7x - 3
=> 18x + 3 = 7x - 3
=> 18x - 7x = -3 - 3
=> 11x = -6
=> x = -6/11
b) -3x(x - 5) + 5(x - 1) + 3x2 = 4x
=> -3x2 + 15x + 5x - 5 + 3x2 = 4x
=> 20x - 5 = 4x
=> 20x - 4x = 5
=> 16x = 5
=> x = 5/16
\(c,7x\left(x-2\right)-5\left(x-1\right)=21x^2-14x^2+3\)
\(\Leftrightarrow7x^2-14x-5x+5=7x^2+3\)
\(\Leftrightarrow7x^2-7x^2-19x=3-5\)
\(\Leftrightarrow-19x=-2\)
\(\Leftrightarrow x=\frac{2}{19}\)
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a, 4x2-5x+1 = 4x2-4x-x+1= 4x(x-1)-(x-1)=(x-1)(4x-1)
c, x2 -6x +8 = x2-2x-4x+8=x(x-2)-4(x-2)=(x-2)(x-4)
e, 3x2 -8x+4 =3x2-6x-2x+4=3x(x-2)-2(x-2)=(x-2)(3x-2)
f,x2 -21x+38=x2-2x-19x+38=x(x-2)-19(x-2)=(x-2)(x-19)
câu b ko rõ đề . câu d thì phương trình đấy vô nghiệm nên bạn xem lại đề nha !
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4x4 - 21 x2y2 + y4
= (4x4 + 4x2y2 + y4) - 25x2y2
= [(2x2)2 + 2x2 . 2 . y2 + (y2)2] - 25x2y2
= (2x2 + y2) - 25x2y2
= (2x2 + y2 - 5xy) (2x2 + y2 + 5xy)
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a: \(\Leftrightarrow4x^3+16x^2+28x-x^2-4x-7+10+a⋮x^2+4x+7\)
hay a=-10