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\(B=\left(x+5\right)\left(2x+6\right)+7\)
\(=2x^2+16x+128-91\)
\(=2\left(x+8\right)^2-91\ge-91\forall x\)
Dấu"=" xảy ra <=>\(2\left(x+8\right)^2=0\Leftrightarrow x=-8\)
Vậy.........
C1: Gọi đa thức thương là Q(x)
Vì x^4 : x^2 = x^2
=> đa thức có dạng x^2+mx+n
Đề x^4 - 3x^2 + ax+b chia hết x^2 - 3x + 2
=> x^4 - 3x^2 + ax + b = (x^2 - 3x + 2)(x^2 + mx + n)
x^4+ 0x^3 - 3x^2 +ax+b = x^4 +mx^3 +(x^2)n -3x^3 -3mx^2 - 3xn + 2x^2 + 2mx + 2n
x^4 + 0x^3 -3x^2 + ax+b = x^4 + x^3(m-3) - x^2(3m - n -2) +x(2m - 3n) +2n
<=>| 0 = m-3 <=> | m = 3
| 3=3m-n-2 | b= 8
| a=2m-3n | n = 4
| b = 2n | a = -6
Vậy a= -6, b= 8
a: \(\Rightarrow10x^2+9x-\left(10x^2+15x-2x-3\right)=8\)
\(\Leftrightarrow10x^2+9x-10x^2-13x+3=8\)
=>-4x=5
hay x=-5/4
b: \(\Leftrightarrow21x-15x^2-35+25x+15x^2-10x+6x-4-2=0\)
=>42x=41
hay x=41/42
b)(2x - 1)^2 - (2x + 5) (2x - 5 ) = 18
4x 2 -4x+1-4x 2+25=18
26-4x=18
4x=8
x=2
a,27x-18=2x-3x^2
<=> 3x^2-2x+27-18x=0
<=> 3x^2-20x+27=0
\(\Delta\)= 20^2-4-12.27
tính \(\Delta\)rồi tìm x1 ,x2
a)(3x-1)(2x+7)-(x+1)(6x-5)=16
=6x^2+21x-2x-7-(6x^2-5x+6x-5)=16
=6x^2+21x-2x-7-6x^2+5x-6x+5=16
=18x-2=16
18x=16+2
18x=18
x=1
vậy x=1
b)(10x+9)x-(5x-1)(2x+3)=8
10x^2+9x-(10x^2+15x-2x-3)=8
10x^2+9x-10x^2-15x+2x+3=8
-4x+3=8
-4x=8-3
-4x=5
x=-5/4.
vay x=-5/4
a: =>17x-5x-15-2x-5=0
=>10x-20=0
=>x=2
b: =>\(\dfrac{3x-6-5x-10}{\left(x+2\right)\left(x-2\right)}=\dfrac{11x+23}{\left(x+2\right)\left(x-2\right)}\)
=>11x+23=-2x-16
=>13x=-39
=>x=-3(nhận)
c: =>5x+7>=3x-3
=>2x>=-10
=>x>=-5
d: =>5(3x-1)=-2(x+1)
=>15x-5=-2x-2
=>17x=3
=>x=3/17
e: =>4x^2-1-4x^2-3x-2=0
=>-3x-3=0
=>x=-1
g: =>7x-5-8x+2-7<0
=>-x-10<0
=>x+10>0
=>x>-10
c. \(\dfrac{x-1}{x-2}+\dfrac{5}{x+2}=\dfrac{12}{x^2-4}+1\\ ĐKXĐ:x\ne2;x\ne-2\\ \Leftrightarrow\dfrac{\left(x-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{12}{\left(x-2\right)\left(x+2\right)}+\dfrac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\\ \Rightarrow x^2+2x-x-2+5x-10=12+x^2-4\\ \Leftrightarrow x^2+2x-x+5x-x^2=12-4+2+10\\ \Leftrightarrow6x=20\\ \Leftrightarrow x=\dfrac{20}{6}\\ \Leftrightarrow x=\dfrac{10}{3}\left(nhận\right)\)
đk : x khác -2 ;2
\(x^2+x-2+5x-10=12+x^2-4\Leftrightarrow6x-12=8\Leftrightarrow x=\dfrac{10}{3}\left(tm\right)\)