a+a x1/3:2/9+a:2/7=252
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a)\(\frac{5}{9}\times x-1=\frac{8}{9}\)
\(\frac{5}{9}\times x=\frac{8}{9}+1\)
\(\frac{5}{9}\times x=\frac{17}{9}\)
\(x=\frac{17}{9}:\frac{5}{9}\)
\(x=\frac{17}{5}\)
B = \(\frac{1}{10.9}+\frac{1}{18.13}+\frac{1}{26.17}+...+\frac{1}{802.405}\)
B = \(\frac{2}{10.18}+\frac{2}{18.26}+\frac{2}{26.34}+...+\frac{2}{802.810}\)
B = \(\frac{1}{4}.\left(\frac{1}{10}-\frac{1}{18}+\frac{1}{18}-\frac{1}{26}+\frac{1}{26}-\frac{1}{34}+...+\frac{1}{802}-\frac{1}{810}\right)\)
B = \(\frac{1}{4}.\left(\frac{1}{10}-\frac{1}{810}\right)=\frac{1}{4}.\frac{8}{81}\)
B = \(\frac{2}{81}\)
\(a+a.\frac{3}{2}+a:\frac{2}{7}=252\)
=>\(a+a.\frac{3}{2}+a.\frac{7}{2}=252\)
=>\(a.\left(1+\frac{3}{2}+\frac{7}{2}\right)=252\)
=>\(a.\left(1+5\right)=252\)
=>\(a.6=252\)
=>\(a=42\)
Vậy a =42
=> a + a x 3/2 +a x 7/2 = 252
=> a x (1 + 3/2 + 7/2) = 252
=> a x 6 = 252
=> a = 252 :6
=> a = 42
Vậy a = 42
Ta có : (x + 2) + (x + 5) + (x + 8) + ...... + (x + 32) = 198
<=> (x + x + x + ...... + x) + (2 + 5 + 8 + ....... + 32) = 198
<=> 11x + 187 = 198
=> 11x = 198 - 187
=> 11x = 11
=> x = 1
4S = 4/(5x5) + 4/(9x9) + … + 1/(409x409)
Ta thấy:
4/(5x5) < 4/(3x7) = 1/3 – 1/7
4/(9x9) < 4/(7x11) = 1/7 – 1/11
…………
4/(409x409) < 4/(407x411) = 1/407 – 1/411
Mà :
4/(3x7) + 4/(7x11) + …. + 4/(407x411) = 1/3 – 1/411 = 136/411
4S < 136/411
S < 34/411 < 34/408 = 1/12
Hay S < 1/12
a ) \(x+x\times\frac{1}{3}\div\frac{2}{9}+x\div\frac{2}{7}=252\)
\(x\times1+x\times\frac{1}{3}\div\frac{2}{9}+x\div\frac{2}{7}=252\)
\(x\times1+x\times\frac{1}{3}\times\frac{9}{2}+x\times\frac{7}{2}=252\)
\(x\times1+x\times\frac{9}{6}+x\times\frac{7}{2}=252\)
\(x\times\left(1+\frac{9}{6}+\frac{7}{2}\right)=252\)
\(x\times6=252\)
\(x=252\div6\)
\(x=42\)
b ) \(\left(3\times x-0,8\right)\div x+14,5=15\)
\(\left(3\times x-0,8\right)\div x=15-14,5\)
\(\left(3\times x-0,8\right)\div x=0,5\)
\(0,8\div x=3-0,5\)
\(0,8\div x=2,5\)
\(x=0,8\div2,5\)
\(x=0,32\)