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M = ( x - 5)( x + 2 ) + ( 3x - 6 )( x + 2 ) - ( 3x - 1/2 )2 + 5x2
= x2-3x-10+3x2-12-(9x2-3x+1/4)+5x2
= x2-3x-10+3x2-12-9x2+3x-1/4+5x2
= 0.x - 89/4
Thay x=2018 => M= -89/4
\(M=\left(x-5\right)\left(x+2\right)+\left(3x-6\right)\left(x+2\right)-\left(3x-\frac{1}{2}\right)^2+5x^2\)
\(M=x^2+2x-5x-10+\left(3x^2+6x-6x-12\right)-\left(9x^2-\frac{3}{2}x+\frac{1}{4}\right)+5x^2\)
\(M=x^2-3x-10+3x^2-12-9x^2+\frac{3}{2}x-\frac{1}{4}+5x^2\)
\(M=-\frac{3}{2}x-\frac{41}{4}\)
Thay x = 2018 vào biểu thức \(M=-\frac{3}{2}x-\frac{41}{4}\), ta có:
\(M=-\frac{3}{2}.2018-\frac{41}{4}=-3027-\frac{41}{4}=\frac{-12149}{4}\)
Vậy giá trị của biểu thức \(M=\left(x-5\right)\left(x+2\right)+\left(3x-6\right)\left(x+2\right)-\left(3x-\frac{1}{2}\right)^2+5x^2\)khi x = 2018 là \(-\frac{12149}{4}\)
a/ ĐKXĐ ....
A=\(\frac{1}{x\left(x-1\right)}+\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-4\right)}+\frac{1}{\left(x-4\right)\left(x-5\right)}\)
=\(\frac{1}{x-1}-\frac{1}{x}+\frac{1}{x-2}-\frac{1}{x-1}+...+\frac{1}{x-5}-\frac{1}{x-4}\)
=\(\frac{1}{x}-\frac{1}{x-5}\)
=\(-\frac{5}{x^2-5x}\)
b/ \(x^3-x+2=0\Leftrightarrow\left(x+1\right)\left(\left(x-1\right)^2+1\right)=0\)
<=> x=-1, thay vào tính nốt
Ta có:
\(A=5x^2-\left[4x^2-3x\left(x-20\right)\right]\)
\(\Leftrightarrow A=5x^2-\left[4x^2-\left(3x^2-60x\right)\right]\)
\(\Leftrightarrow A=5x^2-\left(4x^2-3x^2+60x\right)\)
\(\Leftrightarrow A=5x^2-\left(x^2+60x\right)\)
\(\Leftrightarrow A=5x^2-x^2-60x\)
\(\Leftrightarrow A=4x^2-60x\)
Thay \(x=-\dfrac{1}{2}\) vào biểu thức \(A=4x^2-60x\), ta được:
\(A=4\cdot\left(-\dfrac{1}{2}\right)^2-60\cdot\dfrac{-1}{2}=4\cdot\dfrac{1}{4}+30=31\)
\(A=5x^2-\left[4x^2-3x\left(x-20\right)\right]=5x^2-\left(4x^2-3x^2+60x\right)=5x^2-4x^2+3x^2-60x=4x^2-60x\)Với \(x=\dfrac{-1}{2}\Rightarrow A=4.\left(\dfrac{-1}{2}\right)^2-60.\left(\dfrac{-1}{2}\right)=31\)
Vì dài quá nên mình chỉ có thể trả lời được mấy câu thôi
Bài 1:
27x3 - 8 : (6x + 9x2 +4)
= (3x - 2) (9x2 + 6x + 4) : (9x2 + 6x + 4)
= 3x - 2
Bài 3:
a, 81x4 + 4 = (9x2)2 + 36x2 + 4 - 36x2
= (9x2 + 2)2 - (6x)2
= (9x2 + 6x + 2)(9x2 - 6x + 2)
b, x2 + 8x + 15 = x2 + 3x + 5x + 15
= x(x + 3) + 5(x + 3)
= (x + 3)(x + 5)
c, x2 - x - 12 = x2 + 3x - 4x - 12
= x(x + 3) - 4(x + 3)
= (x + 3) (x - 4)
Câu 1:
(27x3 - 8) : (6x + 9x2 + 4)
= (3x - 2)(9x2 + 6x + 4) : (6x + 9x2 + 4)
= 3x - 2
Câu 2:
a) (3x - 5)(2x+ 11) - (2x + 3)(3x + 7)
= 6x2 + 33x - 10x - 55 - 6x2 - 14x - 9x - 21
= -76
⇒ đccm
b) (2x + 3)(4x2 - 6x + 9) - 2(4x3 - 1)
= 8x3 + 27 - 8x3 + 2
= 29
⇒ đccm
Câu 3:
a) 81x4 + 4
= (9x2)2 + 22
= (9x2 + 2)2 - (6x)2
= (9x2 - 6x + 2)(9x2 + 6x + 2)
b) x2 + 8x + 15
= x2 + 3x + 5x + 15
= x(x + 3) + 5(x + 3)
= (x + 3)(x + 5)
c) x2 - x - 12
= x2 - 4x + 3x - 12
= x(x - 4) + 3(x - 4)
= (x - 4)(x + 3)
Bài 2:
a, \(A=3x\left(2x-5y\right)+\left(3x-y\right)\left(-2x\right)-\dfrac{1}{2}\left(2-26xy\right)\)
\(=6x^2-15xy-6x^2+2xy-1+13xy\)
\(=-1\)
\(\Rightarrowđpcm\)
b, \(B=\left(2x-3\right)\left(4x+1\right)-4\left(x-1\right)\left(2x-1\right)-2x+5\)
\(=8x^2+2x-12x-3-4\left(2x^2-x-2x+1\right)-2x+5\)
\(=8x^2-10x+2-8x^2+4x+8x-4-2x\)
\(=2-4=-2\)
\(\Rightarrowđpcm\)
\(M=\left(x-5\right)\left(x+2\right)+\left(3x-6\right)\left(x+2\right)-\left(3x-\dfrac{1}{2}\right)^2+5x^2\)
\(=\left(x+2\right)\left(x-2+3x-6\right)-\left(9x^2-3x+1\right)+5x^2\) \(=\left(x+2\right)\left(4x-8\right)-9x^2+3x-1+5x^2\) \(=4\left(x+2\right)\left(x-2\right)-4x^2+3x+1\) \(=4\left(x^2-4\right)-4x^2+3x+1\) \(=4x^2-16-4x^2+3x+1\) \(=3x-15\) \(=3\left(x-5\right)\) Với x=2018 thì \(M=3\left(2018-5\right)=3.2015=6045\)