1. Tìm max hoặc min:
a. A = x^2 - 5x - 1
b. B = 1/4x - x + 5.
c. C = x^2 - 4xy + 7y^2 - 2y +3
d. D = 5x^2 - xy + 1/24y^2 + 2x - 1
e. E = x^2 - 3xy + y - 2y - 1
2. Tìm x:
a. ( 2x - 3 )^2 - ( 4x + 1 ).( 4x - 1 ) = ( 2x - 1 ).( 3 - 7x )
b. 1/16x^2 - ( 3x + 5 ) = 0
c. 4.( x - 3 ) - ( x + 2 ) = 0
K
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11 tháng 8 2016
Bài 1:
a. A = x^2 - 5x - 1
\(=x^2-5x+\frac{25}{4}-\frac{29}{4}\)
\(=x^2-5x+\left(\frac{5}{2}\right)^2-\frac{29}{4}\)
\(=\left(x-\frac{5}{2}\right)^2-\frac{29}{4}\ge0-\frac{29}{4}=-\frac{29}{4}\)
Dấu = khi x=5/2
Vậy MinC=-29/4 khi x=5/2
11 tháng 8 2016
2. Tìm x:
a. ( 2x - 3 )^2 - ( 4x + 1 )( 4x - 1 ) = ( 2x - 1 ).( 3 - 7x )
=>4x2-12x+9+1-16x2=-14x2+13x-3
=>-12x2-12x+10=-14x2+13x-3
=>2x2-25x+13=0
\(\Rightarrow2\left(x-\frac{25}{4}\right)^2-\frac{521}{8}=0\)
\(\Rightarrow\left(x-\frac{25}{4}\right)^2=\frac{521}{16}\)
\(\Rightarrow x-\frac{25}{4}=\pm\sqrt{\frac{521}{16}}\)
\(\Rightarrow x=\frac{25}{4}\pm\frac{\sqrt{521}}{4}\)
c. 4.( x - 3 ) - ( x + 2 ) = 0
=>4x-12-x-2=0
=>3x-14=0
=>3x=14
=>x=14/3
21 tháng 1
Bài 1:
a: ĐKXĐ: \(x+4\ne0\)
=>\(x\ne-4\)
b: ĐKXĐ: \(2x-1\ne0\)
=>\(2x\ne1\)
=>\(x\ne\dfrac{1}{2}\)
c: ĐKXĐ: \(x\left(y-3\right)\ne0\)
=>\(\left\{{}\begin{matrix}x\ne0\\y-3\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\y\ne3\end{matrix}\right.\)
d: ĐKXĐ: \(x^2-4y^2\ne0\)
=>\(\left(x-2y\right)\left(x+2y\right)\ne0\)
=>\(x\ne\pm2y\)
e: ĐKXĐ: \(\left(5-x\right)\left(y+2\right)\ne0\)
=>\(\left\{{}\begin{matrix}x\ne5\\y\ne-2\end{matrix}\right.\)
Bài 2:
a: \(\dfrac{-12x^3y^2}{-20x^2y^2}=\dfrac{12x^3y^2}{20x^2y^2}=\dfrac{12x^3y^2:4x^2y^2}{20x^2y^2:4x^2y^2}=\dfrac{3x}{5}\)
b: \(\dfrac{x^2+xy-x-y}{x^2-xy-x+y}\)
\(=\dfrac{\left(x^2+xy\right)-\left(x+y\right)}{\left(x^2-xy\right)-\left(x-y\right)}\)
\(=\dfrac{x\left(x+y\right)-\left(x+y\right)}{x\left(x-y\right)-\left(x-y\right)}=\dfrac{\left(x+y\right)\left(x-1\right)}{\left(x-y\right)\left(x-1\right)}\)
\(=\dfrac{x+y}{x-y}\)
c: \(\dfrac{7x^2-7xy}{y^2-x^2}\)
\(=\dfrac{7x\left(x-y\right)}{\left(y-x\right)\left(y+x\right)}\)
\(=\dfrac{-7x\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{-7x}{x+y}\)
d: \(\dfrac{7x^2+14x+7}{3x^2+3x}\)
\(=\dfrac{7\left(x^2+2x+1\right)}{3x\left(x+1\right)}\)
\(=\dfrac{7\left(x+1\right)^2}{3x\left(x+1\right)}=\dfrac{7\left(x+1\right)}{3x}\)
e: \(\dfrac{3y-2-3xy+2x}{1-3x-x^3+3x^2}\)
\(=\dfrac{3y-2-x\left(3y-2\right)}{1-3x+3x^2-x^3}\)
\(=\dfrac{\left(3y-2\right)\left(1-x\right)}{\left(1-x\right)^3}=\dfrac{3y-2}{\left(1-x\right)^2}\)
g: \(\dfrac{x^2+7x+12}{x^2+5x+6}\)
\(=\dfrac{\left(x+3\right)\left(x+4\right)}{\left(x+3\right)\left(x+2\right)}\)
\(=\dfrac{x+4}{x+2}\)
25 tháng 8 2016
a) 5x2 ( 3x2 -7x+2)-15x(x-3)
=15x4-35x3+10x2-15x2+45x
=15x4-35x3-5x2+45x
c) (x+3)(x-3)(x-2)(x+1)
=(x2-9)(x2+x-2x-2)
=(x2-9)(x2-x-2)
=x4-x3-2x2-9x2+9x+18
=x4-x3-11x2+9x+18
d)(2x+1)2+(4x-1)2+2(2x+1)(4x+1)
=2x2+4x+1-16x2-8x+1
=2x2+4x+1-16x2-8x+1+16x2-4x+8x-2
=2x2+7
e) (2x2-3x)(5x2-2x+1)-10x2(x+3)
=10x4 -4x3+2x2-15x3+6x2-3 -10x2-30x
=10x4-19x3-2x2-30x-3
KV
20 tháng 10 2023
a) Xem lại đề
b) x³ - 4x²y + 4xy² - 9x
= x(x² - 4xy + 4y² - 9)
= x[(x² - 4xy + 4y² - 3²]
= x[(x - 2y)² - 3²]
= x(x - 2y - 3)(x - 2y + 3)
c) x³ - y³ + x - y
= (x³ - y³) + (x - y)
= (x - y)(x² + xy + y²) + (x - y)
= (x - y)(x² + xy + y² + 1)
d) 4x² - 4xy + 2x - y + y²
= (4x² - 4xy + y²) + (2x - y)
= (2x - y)² + (2x - y)
= (2x - y)(2x - y + 1)
e) 9x² - 3x + 2y - 4y²
= (9x² - 4y²) - (3x - 2y)
= (3x - 2y)(3x + 2y) - (3x - 2y)
= (3x - 2y)(3x + 2y - 1)
f) 3x² - 6xy + 3y² - 5x + 5y
= (3x² - 6xy + 3y²) - (5x - 5y)
= 3(x² - 2xy + y²) - 5(x - y)
= 3(x - y)² - 5(x - y)
= (x - y)[(3(x - y) - 5]
= (x - y)(3x - 3y - 5)
18 tháng 10 2021
b: \(B=\dfrac{3y+5}{y-1}-\dfrac{-y^2-4y}{y-1}+\dfrac{y^2+y+7}{y-1}\)
\(=\dfrac{3y+5+y^2+4y+y^2+y+7}{y-1}\)
\(=\dfrac{2y^2+8y+12}{y-1}\)