x + x / 130 + x / 208 + x / 304 + x / 418 + x/ 550 = 1
\(S=\frac{1}{x^2+5x+4}+\frac{1}{x^2+11x28}+\frac{1}{x^2+17x+70}+\frac{1}{x^2+23x+130}+\frac{1}{x^2+29x+208}\)
Tính nhanh.(ai giúp mik với nha! THANKS!)
\(S=\frac{1}{x^2+5x+4}+\frac{1}{x^2+11x+28}+\frac{1}{x^2+17x+70}+\frac{1}{x^2+23x+130}+\frac{1}{x^2+29x+208}\)
\(=\frac{1}{x^2+4x+x+4}+\frac{1}{x^2+7x+4x+28}+...+\frac{1}{x^2+16x+13x+208}\)
\(=\frac{1}{x\left(x+4\right)+\left(x+4\right)}+\frac{1}{x\left(x+7\right)+4\left(x+7\right)}+...+\frac{1}{x\left(x+16\right)+13\left(x+16\right)}\)
\(=\frac{1}{\left(x+1\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+7\right)}+...+\frac{1}{\left(x+13\right)\left(x+16\right)}\)
\(=\frac{1}{3}\left[\frac{3}{\left(x+1\right)\left(x+4\right)}+\frac{3}{\left(x+4\right)\left(x+7\right)}+...+\frac{3}{\left(x+13\right)\left(x+16\right)}\right]\)
\(=\frac{1}{3}\left[\frac{1}{x+1}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+7}+...+\frac{1}{x+13}-\frac{1}{x+16}\right]\)
\(=\frac{1}{3}\left[\frac{1}{x+1}-\frac{1}{x+16}\right]\)\(=\frac{1}{3}\left[\frac{x+16}{\left(x+1\right)\left(x+16\right)}-\frac{x+1}{\left(x+1\right)\left(x+16\right)}\right]\)
\(=\frac{1}{3}\cdot\frac{15}{x^2+17x+16}=\frac{5}{x^2+7x+16}\)
Bài 1: Tính nhanh
\(\frac{1}{x^2+5x+4}+\frac{1}{x^2+11x+28}+\frac{1}{x^2+17x+70}+\frac{1}{x^2+23x+130}+\frac{1}{x^2+29x+208}\)
Bài 2: Tìm a; b; c thỏa mãn đẳng thức: a2 - 2a + b2 + 4b +4c2 - 4c + 6 =0
Bài 1:
\(=\dfrac{1}{\left(x+1\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+7\right)}+\dfrac{1}{\left(x+7\right)\left(x+10\right)}+\dfrac{1}{\left(x+10\right)\left(x+13\right)}+\dfrac{1}{\left(x+13\right)\left(x+16\right)}\)
\(=\dfrac{1}{3}\left(\dfrac{3}{\left(x+1\right)\left(x+4\right)}+\dfrac{3}{\left(x+4\right)\left(x+7\right)}+\dfrac{3}{\left(x+7\right)\left(x+10\right)}+\dfrac{3}{\left(x+10\right)\left(x+13\right)}+\dfrac{3}{\left(x+13\right)\cdot\left(x+16\right)}\right)\)
\(=\dfrac{1}{3}\left(\dfrac{1}{x+1}-\dfrac{1}{x+4}+\dfrac{1}{x+4}-\dfrac{1}{x+7}+\dfrac{1}{x+7}-\dfrac{1}{x+10}+\dfrac{1}{x+10}-\dfrac{1}{x+13}+\dfrac{1}{x+13}-\dfrac{1}{x+16}\right)\)
\(=\dfrac{1}{3}\left(\dfrac{1}{x+1}-\dfrac{1}{x+16}\right)\)
\(=\dfrac{1}{3}\cdot\dfrac{x+16-x-1}{\left(x+1\right)\left(x+16\right)}=\dfrac{5}{\left(x+1\right)\left(x+16\right)}\)
Bài 2:
\(\Leftrightarrow a^2-2a+1+b^2+4b+4+4c^2-4c+1=0\)
\(\Leftrightarrow\left(a-1\right)^2+\left(b+4\right)^2+\left(2c-1\right)^2=0\)
Dấu '=' xảy ra khi a=1; b=-4; c=1/2
3a/4 + 3a/28 + 3a/70 + 3a/130 + ................+ 3a/418 + 3a/550 = 48/25
Giá trị của \(x\) sao cho: 10 x 1 + 10 x 2 + … + 10 x 9 + 10 x 10 = 11 x \(x\) là
a/ 550 b/500 c/ 60 d/ 50
0,54 x 550 + 0,27 x 126 x 2 + 3 x 324 x 0,18
0,54 x 550 + 0,27 x 126 x 2 + 3 x 324 x 0,18
= 0,54 x 550 + ( 0,27 x 2 ) x 126 + ( 3 x 0,18 ) + 324
= 0,54 x 550 + 0,54 x 126 + 0,54 x 324
= 0,54 x ( 550 + 126 + 324 )
= 0,54 x 1000
= 540
0,54 x 550 + 0,27 x 126 x 2 + 3 x 324 x 0,18
0,54 x 550 + 0,27 x 126 x 2 + 3 x 324 x 0,18
= 0,54 x 550 + ( 0,27 x 2 ) x 126 + ( 3 x 0,18 ) + 324
= 0,54 x 550 + 0,54 x 126 + 0,54 x 324
= 0,54 x ( 550 + 126 + 324 )
= 0,54 x 1000
= 540
vừa làm rồi
130 x 2 + 130 x 8
= …………………………………………
= …………………………………………
130 x 2 + 130 x 8
=…………………………………………
=…………………………………………
402 x 9 – 402 x 7 = …………………………………………
= …………………………………………
402 x 9 – 402 x 7
=…………………………………………
=…………………………………………
130 x 2 + 130 x 8
= …………………………………………
= …………………………………………
130 x 2 + 130 x 8
=…………………………………………
=…………………………………………
402 x 9 – 402 x 7
= …………………………………………
= …………………………………………
402 x 9 – 402 7
=…………………………………………
=…………………………………………
130 x 2 + 130 x 8
= 130 x (2+8)
= 130 x 10
= 1300
402 x 9 – 402 x 7
= 402 x (9-7)
= 402 x 2
= 804
a,x+(x+1)+(x+2)+.....+2008+2009=2009
b,x+(x+1)+(x+2)+....=208+209=209
Với sao x + ( x+ 1 ) + ( x + 2 ) Vậy thì các giá trị trong ngoặc sau có x không tkế ???