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a) \(\frac{x-1}{99}+\frac{x-2}{98}+\frac{x-3}{97}+\frac{x-4}{96}=4\)
\(\Rightarrow\frac{x-1}{99}-1+\frac{x-2}{98}-1+\frac{x-3}{97}-1+\frac{x-3}{96}-1=4-4\)
\(\Rightarrow\frac{x-100}{99}+\frac{x-100}{98}+\frac{x-100}{97}+\frac{x-100}{96}=0\)
\(\Rightarrow\left(x-100\right)\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+\frac{1}{96}\right)=0\)
\(\Rightarrow x-1=0\) ( vì \(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+\frac{1}{96}\ne0\) )
Vậy x = 1
b) \(\frac{x+1}{99}+\frac{x+2}{98}+\frac{x+3}{97}=3\)
\(\Rightarrow\frac{x+1}{99}+1+\frac{x+2}{98}+1+\frac{x+3}{97}+1=3-3\)
\(\Rightarrow\frac{x+100}{99}+\frac{x+100}{98}+\frac{x+100}{97}=0\)
\(\Rightarrow\left(x+100\right).\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}\right)=0\)
Vì \(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}\ne0\)
=> x + 100 = 0
=> x = -100
c) \(\frac{x-1}{99}+\frac{x-2}{49}+\frac{x-4}{32}=6\)
\(\Rightarrow\frac{x-1}{99}-1+\frac{x-2}{49}-2+\frac{x-4}{32}-3=6-6\)
\(\Rightarrow\frac{x-100}{99}+\frac{x-100}{49}+\frac{x-100}{32}=0\)
\(\Rightarrow\left(x-100\right)\left(\frac{1}{99}+\frac{1}{49}+\frac{1}{32}\right)=0\)
Vì \(\frac{1}{99}+\frac{1}{49}+\frac{1}{32}\ne0\)
=> x - 100 = 0
=> x = 100
Chúc bạn học tốt
có người khác trả lời trước rồi nên chị ko trả lời đâu nhé em trai
a)|x|-7=-5
|x|=-5+7
|x|=2
=> x= 2 hoặc x=-2
b)12-|x|=5
|x| = 12 - 5
|x| = 7
=> x= 7 hoặc x= -7
c)|x+3|=4
=> x+3=4 hoặc x+3=-4
x=4-3 x=-4-3
x=1 x=-7
vậy x=1 hoặc x=-7
d)|x+8|=|-6|
|x+8|=6
=>x+8=6 hoặc x+8=-6
x=6-8 x=-6-8
x=-2 x=-14
vậy x=-2 hoặc x=-14
a)|x|-7=-5
/x/ = (-5) + 7
/x/ = 2
=> x = 2 hoặc x = -2
b)12-|x|=5
/x/ = 12 - 5
/x/ = 7
=> x = 7 hoặc x = -7
c)|x+3|=4
x + 3 = 4 hoặc x + 3 = -4
x = 4 - 3 x = (-4) - 3
x = 1 x = -1
d)|x+8|=|-6|
/x+ 8 / = 6
x + 8 = 6 hoặc x + 8 = -6
x = 6-8 x = (-6) - 8
x = -2 x = -14
\(a)24\times(x-16)=12^2\\\Rightarrow 24\times(x-16)=144\\\Rightarrow x-16=144:24\\\Rightarrow x-16=6\\\Rightarrow x=6+16\\\Rightarrow x=22\\---\\b)(x^2-10):5=5\\\Rightarrow x^2-10=5\times5\\\Rightarrow x^2-10=25\\\Rightarrow x^2=25+10\\\Rightarrow x^2=35\\\Rightarrow x=\pm\sqrt{35}\\---\)
\(c)(5x+335):2=400\\\Rightarrow 5x+335=400\times2\\\Rightarrow 5x+335=800\\\Rightarrow 5x=800-335\\\Rightarrow 5x=465\\\Rightarrow x=465:5\\\Rightarrow x=93\\---\\d)63:(5x+4)=2^3-1\\\Rightarrow 63:(5x+4)=8-1\\\Rightarrow 63:(5x+4)=7\\\Rightarrow 5x+4=63:7\\\Rightarrow 5x+4=9\\\Rightarrow 5x=9-4\\\Rightarrow 5x=5\\\Rightarrow x=5:5\)
\(\Rightarrow x=1\)
\(Toru\)
a, 1 - 2 - 3 + 4 + 5 + 6 - 7 + ... + 1996 + 1997 - 1998 - 1999 + 2000 + 2001
= ( 1 - 2 - 3 + 4 ) + ( 5 - 6 - 7 + 8 ) + ... +( 1993 - 1994 - 1995 + 1996 ) + ( 1997 - 1998 - 1999 + 2000 ) + 2001
= 0 + 0 + ... + 0 + 0 + 2001
= 2001
b, 1 - 3 + 5 -7 + ...+ 2001 - 2003 + 2005
= ( 1 -3 ) + ( 5 - 7 ) + ... + ( 2001 - 2003 ) + 2005
= -2 + (-2 )+ ... + (-2) + 2005
Có 501 số ( - 2 )
= ( - 2 ) . 501 + 2005
= -1002 + 2005
= 1003
P/s : Tham khảo ( Chép đầu bài thôi cũng sai )
từ đề bài:
=> \(\frac{a}{b}=\frac{3}{4}\Rightarrow\frac{a}{3}=\frac{b}{4}\Rightarrow\frac{a}{15}=\frac{b}{20}\left(1\right)\)
\(\frac{b}{c}=\frac{5}{6}\Rightarrow\frac{b}{5}=\frac{c}{6}\Rightarrow\frac{b}{20}=\frac{c}{24}\left(2\right)\)
\(\frac{c}{d}=\frac{8}{9}\Rightarrow\frac{c}{8}=\frac{d}{9}\Rightarrow\frac{c}{24}=\frac{d}{27}\left(3\right)\)
Từ 1 ; 2 ; 3
=> \(\frac{a}{15}=\frac{b}{20}=\frac{c}{24}=\frac{d}{27}=\frac{a+b+c+d}{15+20+24+27}=\frac{172}{86}=2\)
\(\frac{a}{15}=2\Rightarrow a=30\)
\(\frac{b}{20}=2\Rightarrow b=40\)
\(\frac{c}{24}=2\Rightarrow c=48\)
\(\frac{d}{27}=2\Rightarrow d=54\)
từ a/b=3/4=>4a=3b=>a/3=b/4=>a/15=b/20(1)
b/c=5/6=>6b=5c=>b/5=c/6=>b/20=c/24(2)
c/d=8/9=>9c=8d=>c/8=d/9=>c/24=d/27(3)
từ (1),(2),(3)=> a/15=b/20=c/24=d/27=K (K khác 0)
=>a=15K;b=20K;c=24K;d=27K
mà a+b+c+d=172
hay 15K+20K+24K+27K=172
k+(15+20+24+27)=172
K+86=172
=>K=172:86
K=2
=>a=30;b=40;c=48;d=54
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