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a) \(a^2+b^2+c^2=ab+bc+ca\)
\(\Leftrightarrow2\left(a^2+b^2+c^2\right)=2ab+2bc+2ca\)
\(\Leftrightarrow\left(a^2-2ab+b^2\right)+\left(b^2-2bc+c^2\right)+\left(c^2-2ca+a^2\right)=0\)
\(\Leftrightarrow\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(a-b\right)^2=0\\\left(b-c\right)^2=0\\\left(c-a\right)^2=0\end{cases}}\Leftrightarrow a=b=c\)
Mà a + b + c = 3 \(\Rightarrow a=b=c=1\)
\(\Rightarrow M=1+2015+2020\)\(=4036\)
b) \(\frac{x-y}{x+y}< \frac{x^2-y^2}{x^2+y^2}\)
\(\Rightarrow\left(x-y\right)\left(x^2+y^2\right)< \left(x+y\right)\left(x^2-y^2\right)\)
\(\Leftrightarrow\left(x-y\right)\left(x^2+y^2\right)-\left(x+y\right)\left(x-y\right)\left(x+y\right)< 0\)
\(\Leftrightarrow\left(x-y\right)\left[x^2+y^2-\left(x+y\right)\left(x+y\right)\right]< 0\)
\(\Leftrightarrow\left(x-y\right)\left(x^2+y^2-x^2-2xy-y^2\right)< 0\)
\(\Leftrightarrow-2xy\left(x-y\right)< 0\)
Có \(x>y\Rightarrow x-y>0\)
\(\Rightarrow-2xy< 0\)
\(\Leftrightarrow xy>0\)
TH1: \(\orbr{\begin{cases}x>0\\y>0\end{cases}}\)( thỏa mãn )
TH2:\(\orbr{\begin{cases}x< 0\\y< 0\end{cases}}\)( loại )
Vậy bđt được chứng minh
A = 4x2 - 12x + 13
= (4x2 - 12x + 9) + 4
= 4(x2 - 3x + \(\frac{9}{4}\) ) + 4
A = 4(x - \(\frac{3}{2}\) )2 + 4
Vì : (x - \(\frac{3}{2}\) )2 \(\ge0\forall x\)
Nên : 4(x - \(\frac{3}{2}\) )2 \(\ge0\forall x\)
Vậy A = 4(x - \(\frac{3}{2}\) )2 + 4 \(\ge4>0\forall x\)
a) \(\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+17}{83}+\frac{x+116}{4}=0\)
\(\Leftrightarrow\)\(\frac{x+14}{86}+1+\frac{x+15}{85}+1+\frac{x+16}{84}+1+\frac{x+17}{83}+1+\frac{x+116}{4}-4=0\)
\(\Leftrightarrow\)\(\frac{x+100}{86}+\frac{x+100}{85}+\frac{x+100}{84}+\frac{x+100}{83}+\frac{x+100}{4}=0\)
\(\Leftrightarrow\)\(\left(x+100\right)\left(\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4}\right)=0\)
\(\Leftrightarrow\)\(x+100=0\)
\(\Leftrightarrow\)\(x=-100\)
Vậy...
a) \(75.20,9+5^2.20,9\)
\(=20,9\left(75+5^2\right)\)
\(=20,9\left(75+25\right)\)
\(=20,9.100\)
\(=2090\)
b) \(86.15+150.1,4\)
\(=15\left(86+10.1,4\right)\)
\(=15\left(86+14\right)=15.100=1500\)
c) \(93.32+14.16\)
\(=16\left(93.2+14\right)\)
\(=16\left(186+14\right)=16.200=3200\)
d) \(98,6.199-990.9,86\)
\(=9,86\left(10.199-990\right)=9,86\left(1990-990\right)\)
\(=9,86.1000=9860\)
e) \(-8.40+2.108+24\)
\(=-8.40+2.4.27+8.3\)
\(=-8\left(40-27-3\right)=-8.10=-80\)
a) x(y + 4) + 3(y + 4) = 19
<=> (y + 4)(x + 3) = 19
| x + 3 | 19 | 1 | -1 | -19 |
| y + 4 | 1 | 19 | -19 | -1 |
| x | 16 | -2 | -4 | - 22 |
| y | -3 | 15 | -23 | -5 |
pn kẻ bảng ghi y + 4 trước nha, xách hàng 2 lên hàng đầu, hàng 4 lên hàng 3
b) xy + 3x - 2y - 7 = 0
xy + 3x - 2y - 6 = 1
x(y + 3) - 2(y + 3)= 1
(y + 3)(x - 2) = 1
| y + 3 | - 1 | 1 |
| x - 2 | - 1 | 1 |
| y | - 4 | - 2 |
| x | 1 | 3 |
c) 2y(x + 3) = x + 13
2xy + 6y = x + 13
2xy - x + 6y - 3 = 10
x(2y - 1) + 3(2y - 1) = 10
(2y - 1)(x + 3) = 10
tới đây pn lm tương tự như mấy câu kia
d) y(x - 2) + 3x - 6 = 2
y(x - 2) + 3(x - 2) = 2
(x - 2)(y + 3) = 2
| x - 2 | - 1 | - 2 | 1 | 2 |
| y + 3 | -2 | -1 | 2 | 1 |
| x | 1 | 0 | 3 | 4 |
| y | -5 | -4 | -1 | -1 |
e) xy - x + 5y - 7 = 0
xy - x + 5y - 5 = 2
x(y - 1) + 5(y - 1) = 2
(y - 1)(x + 5) = 2
| y - 1 | - 2 | - 1 | 2 | 1 |
| x + 5 | - 1 | - 2 | 1 | 2 |
| y | -1 | 0 | 3 | 2 |
| x | -6 | -7 | -4 | - 3 |
A = 2x2 - 6xy - 3xy - 6y - 2x2 + 8xy + 6y
= - xy
= \(\frac{2}{3}\)\(x\)\(\frac{3}{4}\)
= \(\frac{1}{2}\)
mk đang bận mấy câu kia tương tự nha
a) 86.53=4558
b) 33.44=1452
c) 157.24=3768
d) 1122.19=21318
86 x 53 = 4558
33 x 44 = 1452
157 x 27 = 3768
1122 x 19 = 21318