Tính nhanh
2017 x 34 + 2017 x 65 + 2017
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a) 2017 x 34 + 2017 x 65 + 2017
= 2017 x ( 34+65+1)
= 2017 x 100
= 201700
b) 3/5 x 7/9 - 3/5 x 2/9
= 3/5 x ( 7/9- 2/9)
= 3/5 x 5/9
= 1/3
a) 2017 x 34 + 2017 x 65 + 2017
= 2017 x (34 + 65 + 1)
= 2017 x 100
= 201700
b) \(\dfrac{3}{5}\) x \(\dfrac{7}{9}\) - \(\dfrac{3}{5}\) x \(\dfrac{2}{9}\)
= \(\dfrac{3}{5}\) x \(\left(\dfrac{7}{9}-\dfrac{2}{9}\right)\)
= \(\dfrac{3}{5}\) x \(\dfrac{5}{9}\)
= \(\dfrac{1}{3}\)
Tính nhanh:
a) 36.(65-79)+65|35-79|
=36.(-14) + 65.44
=-504 + 2860
=2356
b) 12.(34-86)+34.(86-12)+86.(12-34)-12.(34+86)
= 12.(-52) +34.74+86. (-22) - 12.120
=-624 + 2516 +(-1892) -1440
= 1892 + (-1892) -1440
=0- 1440
=-1440
32 x 27 + 148 x 34 + 16 x 94
= ( 32 x 27 + 16 x 94 ) + 74 * 2 * 34
= 32 ( 27 + 47 ) + 74 x 68
= 32 x 74 + 74 x 68
= ( 32 + 68 ) x 74
= 100 * 74
= 7400
\(\frac{2017\cdot2013-2017}{4034\cdot1006+2007}\)
\(=\frac{2017\cdot\left(2013-1\right)}{2017\cdot\left(2012+1\right)}\)
\(=\frac{2012}{2013}\)
Ta có : \(4x^2+2y^2+2z^2-4xy-4zx+2yz-6y-10z+34=0\)
\(\Rightarrow\left(4x^2+y^2+z^2-4xy-4zx+2yz\right)+\left(y^2-6y+9\right)+\left(z^2-10z+25\right)=0\)
\(\Rightarrow\left(2x-y-z\right)^2+\left(y-3\right)^2+\left(z-5\right)^2=0\)
Vì \(\hept{\begin{cases}\left(2x-y-z\right)^2\ge0\forall x,y,z\\\left(y-3\right)^2\ge0\forall y\\\left(z-5\right)^2\ge0\forall z\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}\left(2x-y-z\right)^2=0\\\left(y-3\right)^2=0\\\left(z-5\right)^2=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x-y-z=0\\y-3=0\\z-5=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x-3-5=0\\y=3\\z=5\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x=8\\y=3\\z=5\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=4\\y=3\\z=5\end{cases}}\left(1\right)\)
Lại có : \(S=\left(x-4\right)^{2017}+\left(y-4\right)^{2017}+\left(z-4\right)^{2017}\)
Thay \(\left(1\right)\)vào \(S\),ta được :
\(S=0^{2017}+\left(-1\right)^{2017}+1^{2017}\)
\(=0-1+1=0\)
Vậy \(S=0\)
a) (17.x - 25 ) : 8 = 92 : 65= 92/65
17x - 25 = 92/65.8
17x = 2361/65
x= 2361/65 : 17=2361/1105
b) x- 60 = 2017101 - 2017100
x-60 = 2017
x = 2017 + 60
x = 2077
c) 5x . 30-3x.x = 45
5x.3x.x = 45 + 30 = 75
15x.x = 75
B) 2017100.(x-60)=2017101
x-60=2017101 : 2017100
x-60 = 2017
x= 2017 + 60
x= 2077
C) 5.x+3.(10-x)+x=45
5x+30 - 3x + x = 45
3x = 45-30
3x = 15
x= 5
A) (17x-25):8+65=92
(17x-25):8 = 81 - 65
(17x-25):8 = 16
17x-25= 16:8
17x = 2+27
17x = 29
x= 29/17
2017 x 7 - 2017 x 4 - 2017 x 3 + 2017
=2017.(7-4-3)
=2017.0
=0
\(2017\times7-2017\times4-2017\times3+2017\)
\(=2017\times(7-4-3+1)\)
\(=2017\times1=2017\)