x + ( x + 1 ) + ( x + 2 ) + ... + ( x + 10 ) = 505
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\(\dfrac{16}{27}xX=\dfrac{10}{27}-\dfrac{6}{27}\)
\(\dfrac{16}{27}xX=\dfrac{4}{27}\)
\(X=\dfrac{4}{27}:\dfrac{16}{27}\)
X=\(\dfrac{1}{4}\)
16/27x X+2/9=10/27
16/27x X=10/27-2/9
16/27x X=4/27
X=4/27:16/27
X=1/4
\(\dfrac{1}{2}\left(x-2\right)+\dfrac{1}{3}\left(2-x\right)=x\\ \Leftrightarrow\dfrac{1}{2}\left(x-2\right)-\dfrac{1}{3}\left(x-2\right)=x\\ \Leftrightarrow\left(x-2\right).\left(\dfrac{1}{2}-\dfrac{1}{3}\right)=x\\ \Leftrightarrow\left(x-2\right).\left(\dfrac{3-2}{6}\right)=x\\ \Leftrightarrow\left(x-2\right).\dfrac{1}{6}=x\\ \Leftrightarrow\dfrac{1}{6}x-\dfrac{1}{3}-x=0\\ \Leftrightarrow\left(\dfrac{1}{6}-1\right)x=\dfrac{1}{3}\\ \Leftrightarrow\left(\dfrac{1-6}{6}\right)x=\dfrac{1}{3}\\ \Leftrightarrow\dfrac{-5}{6}x=\dfrac{1}{3}\\ \Leftrightarrow x=\dfrac{1}{3}:\left(-\dfrac{5}{6}\right)\\ \Leftrightarrow x=-\dfrac{2}{5}\)
Vậy \(x=-\dfrac{2}{5}\)
(x-2)(y+1)=-4
⇔xy+x-2y-2=-4
⇔-31+x-2y-2=-4
⇔x-2y=4+2+31
⇔x-2y=39
⇔x=39+2y
⇔y=x-39 / 2
1)ta có x.y=23=1.23=(-1)(-23)⇒các cặp (x,y)là(1,23);(23,1);(-1,-23);(-23;-1)
vậy......
2) ta có:(x-1 ).(y+2)= -4=-1.4=1.(-4)=-2.2=2.(-2)
⇒th1:x-1=-1 y+2=4
x=-1+1=0 y=4-2=2
th2:x-1=1 y+2=-4
x=1+1=2 y=-4-2=-6
th3:x-1=-2 y+2=2
x=-2+1=-1 y=2-2=0
th4:x-1=2 y+2=-2
x=2+1=3 y=-2-2=-4
vậy các cặp (x,y)là(0,2);(2,-6);(-1,0);(3,-4)
\(\dfrac{x^2+3x-4}{x-1}=\dfrac{x^2+4x-x-4}{\left(x-1\right)}=\dfrac{\left(x+4\right)\left(x-1\right)}{x-1}=x+4\)
(x-1)/2015 + x/2014 + 1/503 - (x-3)/2013 - x/2012 - 1/1007 =0
(x-2016)/2015 + (x-2016)/2014 - (x-2016)/2012 - (x-2016)/2013 = 0
(x-2016) ( 1/2015 + 1/2016 - 1/2013 - 1/2012) = 0
Mà 1/2015 + 1/2016 - 1/2013 - 1/2012 khác 0
Suy ra x -2016=0
x=2016
Chỗ nào thắc mắc nhớ hỏi mik nhe!
Bài 1 :
A = 12 + 22 + 32 +....+n2
A = 12 + 2.(1+1) + 3.(2 +1) + 4.( 3 +1) +.....+n(n-1 + 1)
A = 1 + 1.2 + 2 + 2.3 + 3 + 3.4 + 4 +.....+ n.(n-1) + n
A = ( 1 + 2 + 3 + 4 +....+n) + ( 1.2 + 2.3 + 3.4 +....+(n-1).n
A = (n+1).{(n-1):n+1)/2 +1/3.[1.2.3 +2.3.3 +.....+(n-1)n.3]
A = (n+1).n/2+1/3.[1.2.3 +2.3.(4-1)+ ...+(n-1).n [(n+1) - (n -2)]
A = (n+1)n/2+1/3.( 1.2.3 + 2.3.4 -1.2.3 +..+ (n-1)n(n+1)- (n-2)(n-1)n)
A =(n+1)n/2 + 1/3.(n-1)n(n+1)
A = n(n+1)[1/2 + 1/3 .(n-1)]
A = n.(n+1) \(\dfrac{3+2n-2}{6}\)
A= n.(n+1)(2n+1)/6
Bài 2 :
a, (x+1) +(x+2) + (x+3)+...+(x+10) = 5070
(x+10 +x+1).{( x+10 - x -1): 1 +1):2 = 5070
(2x + 11)10 : 2 = 5070
( 2x + 11)5 = 5070
2x+ 11 = 5070:5
2x = 1014 - 11
2x = 1003
x = 1003 :2
x = 501,5
b, 1 + 2 + 3 +...+x = 820
( x + 1)[ (x-1):1 +1] : 2 = 820
(x +1).x = 820 x 2
(x +1).x = 1640
(x +1) .x = 40 x 41
x = 40
Có \(\frac{x}{y}=\frac{7}{10}\Rightarrow\frac{x}{7}=\frac{y}{10}\) . Áp dụng tính chất dãy tỉ số bằng nhau, ta có :
\(\frac{x}{7}=\frac{y}{10}=\frac{x+y}{7+10}=\frac{34}{17}=2\) . Từ đó ta suy ra được
\(\Rightarrow x=2.7=14\) \(\Rightarrow y=2.10=20\)
x+(x+1)+(x+2)+...+(x+10)=505
11x+(1+2+...+10)=505
11x+[(10+1).10:2]=505
11x+55=505
11x=450
x=\(\dfrac{450}{11}\)
Vậy \(x=\dfrac{450}{11}\)
x + (x + 1) + (x + 2) + ... + (x + 10) = 505
(x + x + ... + x) + (1 + 2 + 3 + ... + 10) = 505
11x + 55 = 505
11x = 505 - 55
11x = 450
x = 450 : 11
x = `450/11`