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5 tháng 12 2017
1)⇔x2+1x-3x+3=0
⇔x(x+1)-3(x+1)=0
⇔(x+1)(x-3)=0
⇔x+1=0 hoặc x-3=0
⇔x=-1 hoặc x=3
5 tháng 12 2017
4)⇔x(1+5x)=0
⇔x=0 hoặc 1+5x=0
⇔x=0 hoặc 5x=-1
⇔x=0 hoặc x=-0.2
QH
2
15 tháng 9 2018
\(\text{a) x^2 - 5x +10}=x^2-2.\dfrac{5}{2}x+\dfrac{25}{4}-\dfrac{25}{4}+10\)
=\(x^2-2.\dfrac{5}{2}x+\left(\dfrac{5}{2}\right)^2-\left(\dfrac{25}{4}-10\right)\)
=\(\left(x-\dfrac{5}{2}\right)^2-\left(-\dfrac{15}{4}\right)=\left(x-\dfrac{5}{2}\right)^2+\dfrac{15}{4}\)
do (x-5/2)2 \(\ge\)0 với mọi x
=> (x-5/2)2+5/2 >0 với mọi x
=> bthuc luôn dương
11 tháng 12 2022
a: \(=\dfrac{6x^2-3x+4x^2+2x}{\left(2x-1\right)\left(2x+1\right)}\cdot\dfrac{\left(2x-1\right)^2}{2x\left(4x+5\right)}\)
\(=\dfrac{10x^2+x}{\left(2x+1\right)}\cdot\dfrac{2x-1}{2x\left(4x+5\right)}\)
\(=\dfrac{\left(10x^2+x\right)\left(2x-1\right)}{2x\cdot\left(2x+1\right)\left(4x+5\right)}\)
b: \(=\left(\dfrac{x}{\left(5x-1\right)\left(5x+1\right)}\cdot\dfrac{x\left(5x+1\right)}{5x}\right)\cdot\dfrac{x\left(5x+1\right)}{5x-1}+\dfrac{x}{5x-1}\)
\(=\dfrac{x}{5\left(5x-1\right)}\cdot\dfrac{x\left(5x+1\right)}{5x-1}+\dfrac{x}{5x-1}\)
\(=\dfrac{x^2\left(5x+1\right)+5x\left(5x-1\right)}{5\left(5x-1\right)^2}\)
\(=\dfrac{5x^3+x^2+25x^2-5x}{5\left(5x-1\right)^2}=\dfrac{5x^3+26x^2-5x}{5\left(5x-1\right)^2}\)
c: \(=\dfrac{x+1}{x-2}+\dfrac{1-3x}{x\left(x^2+1\right)}\cdot\dfrac{x^2+1}{x-1}\)
\(=\dfrac{x+1}{x-2}+\dfrac{1-3x}{x\left(x-1\right)}\)
\(=\dfrac{x^3-x+\left(1-3x\right)\left(x-2\right)}{x\left(x-1\right)\left(x-2\right)}\)
\(=\dfrac{x^3-x+x-2-3x^2+6x}{x\left(x-1\right)\left(x-2\right)}=\dfrac{x^3-3x^2+6x-2}{x\left(x-1\right)\left(x-2\right)}\)
26 tháng 12 2018
1,4x2.(5x3+2x-1)
=4x2.5x3+4x2.2x-4x2.1
20x5+8x3-4x2
2,4x3y2:x2
=4xy2
3,(15x2y3-10x3y3+6xy):5xy
15x2y3:5xy-10x3y3:5xy+6xy:5xy
3xy2-2x2y2+\(\dfrac{6}{5}\)
13 tháng 12 2022
1: \(=20x^5+8x^3-4x^2\)
2: \(=4xy^2\)
3: \(=3xy^2-2x^2y^2+\dfrac{6}{5}\)
4: \(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}=5x^2+4x+4\)
5: \(=\dfrac{7}{2x}+\dfrac{11}{3y^2}=\dfrac{21y^2+22x}{6xy^2}\)
6: \(=\dfrac{4x^2-7x+3}{\left(4x-7\right)\left(x+2\right)}\)
7: \(=\dfrac{3x+3y-2x^3+2x^2y}{\left(x-y\right)\left(x+y\right)}\)
8: \(=\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)=2x^4y^2-\dfrac{1}{2}x^2y^4\)
9: \(=\left(x-\dfrac{1}{4}\right)\left(4x-1\right)=4\left(x-\dfrac{1}{4}\right)^2=4\left(x^2-\dfrac{1}{2}x+\dfrac{1}{16}\right)\)
\(=4x^2-2x+\dfrac{1}{4}\)
10: \(=\dfrac{3x^2+6-x}{x\left(2x+6\right)}=\dfrac{2x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)
11: \(=\dfrac{x+1}{2}-\dfrac{3}{x-1}\)
\(=\dfrac{x^2-7}{2\left(x-1\right)}\)
12: \(=\dfrac{x^2-xy}{\left(x-y\right)\left(x+y\right)}=\dfrac{x}{x+y}\)
15:=x^3-y^3+2
13 tháng 12 2022
1: \(=20x^5+8x^3-4x^2\)
2: \(=4xy^2\)
3: \(=3xy^2-2x^2y^2+\dfrac{6}{5}\)
4: \(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}=5x^2+4x+4\)
5: \(=\dfrac{7}{2x}+\dfrac{11}{3y^2}=\dfrac{21y^2+22x}{6xy^2}\)
6: \(=\dfrac{4x^2-7x+3}{\left(4x-7\right)\left(x+2\right)}\)
7: \(=\dfrac{3x+3y-2x^3+2x^2y}{\left(x-y\right)\left(x+y\right)}\)
8: \(=\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)=2x^4y^2-\dfrac{1}{2}x^2y^4\)
9: \(=\left(x-\dfrac{1}{4}\right)\left(4x-1\right)=4\left(x-\dfrac{1}{4}\right)^2=4\left(x^2-\dfrac{1}{2}x+\dfrac{1}{16}\right)\)
\(=4x^2-2x+\dfrac{1}{4}\)
10: \(=\dfrac{3x^2+6-x}{x\left(2x+6\right)}=\dfrac{2x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)
11: \(=\dfrac{x+1}{2}-\dfrac{3}{x-1}\)
\(=\dfrac{x^2-7}{2\left(x-1\right)}\)
12: \(=\dfrac{x^2-xy}{\left(x-y\right)\left(x+y\right)}=\dfrac{x}{x+y}\)
15:=x^3-y^3+2
13 tháng 7 2018
Mình giải từ cuối lên , mình giải dần -)
n, <=> x(2x-1)-3(2x-1)=0
<=> (x-3)(2x-1)=0
<=> x= 3 hoặc x= 1/2
m, <=> (x+2)(x2-3x+5)-x2(x+2)=0
<=> (x+2)(x2-3x+5-x2)=0
<=> (x+2)(5-3x)=0
=> x= -2 hoặc5/3
22 tháng 8 2018
\(1.5x\left(x^2+2x-1\right)-3x^2\left(x-2\right)=5x^3+10x^2-5x-3x^3+6x^2\)
\(=2x^3+16x^2-5x\)
\(=\left(2x^3-x\right)+\left(16x^2-4x\right)\)
\(=x\left(2x^2-1\right)+4x\left(4x-1\right)\left(ĐCCM\right)\)