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a, x + 1/2 = 3/2
x = 3/2 - 1/2
x = 1
b, x * 2 + x = 100 * 3
x * ( 2 + 1 ) = 300
x * 3 = 300
x = 300 : 3
x = 100
Áp dụng công thức \(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\) ta đc:
\(\frac{2x+5}{x+5}=\frac{6}{4}\)( . là dấu nhân nha )
\(4\left(2x+5\right)=6\left(x+5\right)\)
\(8x+20=6x+30\)
\(2x=10\)
\(\Rightarrow x=5\)
Ta có:
\(D=1.2+2.3+3.4+4.5+...+99.100\)
\(\Leftrightarrow3D=1.2.\left(3-0\right)+2.3+\left(4-1\right)+3.4+\left(5-2\right)+4.5.\left(6-3\right)+...+99.100.\left(101-98\right)\)
\(\Leftrightarrow3D=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100\)
\(\Leftrightarrow3D=99.100.101\Leftrightarrow D=\frac{99.100.101}{3}=333300\)
\(B=1.3+2.4+3.5+4.6+...+99.101\)
\(\Leftrightarrow B=\left(1.3+3.5+...+99.101\right)+\left(2.4+4.6+...+98.100\right)\)
\(\Leftrightarrow6B=\left(1.3.\left(5-\left(-1\right)\right)+3.5.\left(7-1\right)+...+99.101.\left(103-97\right)\right)+\left(2.4.\left(6-0\right)+4.6.\left(8-2\right)+...+98.100.\left(102-96\right)\right)\)
\(\Leftrightarrow B=\frac{99.101.103+3}{6}+\frac{98.100.102}{6}=338250\)
Vì các bước gần tương tự như bài a) nên mình bỏ bước.
\(C=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\)
\(\Leftrightarrow C=\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)
\(\Leftrightarrow C=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(\Leftrightarrow C=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{49.50}\right)=\frac{1}{2}.\frac{612}{1225}=\frac{306}{1225}\)
\(x+x+x\times2+x\times4+x\times2=2016\)
\(x\times1+x\times1+x\times2+x\times4+x\times2=2016\)
\(x\times\left(1+1+2+4+2\right)=2016\)
\(x\times10=2016\)
\(x=2016\div10\)
\(x=201,6\)
= \(\frac{1x1x1}{1x2x4}x\frac{2.2.1}{1.1.2.2}=\frac{1}{8}.1=\frac{1}{8}\)
=1X2X3/1X2X3X4X2= 1/8 =3X2X2X2X5/3X2X2X5X2= 1/1
=1/8X1/1=1/8
a) \(124+\left(118+x\right)=217\)
\(118+x=217-124\)
\(118+x=93\)
\(x=-25\)
vay \(x=-25\)
b) \(\left[\left(6x-72\right):2-84\right].28=5628\)
\(\left(6x-72\right):2-84=5628:28\)
\(\left(6x-72\right):2-84=201\)
\(\left(6x-72\right):2=201+84\)
\(\left(6x-72\right):2=285\)
\(6x-72=285.2\)
\(6x-72=570\)
\(6x=642\)
\(x=107\)
vay \(x-107\)
c) \(71.2-\left(2x+5\right).6=100\)
\(142-\left(2x+5\right).6=100\)
\(\left(2x+5\right).6=142-100\)
\(\left(2x+5\right).6=42\)
\(2x+5=7\)
\(2x=2\)
\(x=1\)
vay \(x=1\)
\(\frac{1.2.6.4.6.4.5.2}{2.3.6.8.6.2.2.2.8.10}=\frac{1}{96}\)
kết quả x = 97
2x + 6 = 100 x 2
2x = 200 - 6
2x = 194
x = 194 : 2
x = 97