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\(\dfrac{1.3.5+2.6.10+4.12.20+7.21.35}{1.5.7+2.10.14+4.20.28+7.35.49}\)
\(=\dfrac{1.3.5+2^3.1.3.5+2^6.1.3.5+7^3.1.3.5}{1.5.7+2^3.1.5.7+2^6.1.5.7+7^3.1.5.7}\)
\(=\dfrac{1.3.5\left(1+2^3+2^6+7^3\right)}{1.5.7\left(1+2^3+2^6+7^3\right)}\)
\(=\dfrac{1.3.5}{1.5.7}\)
\(=\dfrac{3}{7}\)
Ta có : \(\dfrac{1.3.5+2.6.10+4.12.20 +7.21.35 }{1.5.7+2.10.14+4.20.28+7.35.49}\)
\(=\dfrac{1.3.5+1.2.3.2.5.2+1.4.3.4.5.4+1.7.3.7.5.7}{1.5.7+1.2.5.2.7.2+1.4.5.4.7.4+1.7.5.7.7.7}\)
\(=\dfrac{1.\left(1.3.5\right)+2.\left(1.3.5\right)+4.\left(1.3.5\right)+7.\left(1.3.5\right)}{1.\left(1.5.7\right)+2.\left(1.5.7\right)+4.\left(1.5.7\right)+7.\left(1.5.7\right)}\)
\(=\dfrac{1.3.5.\left(1+2+4+7\right)}{1.5.7.\left(1+2+4+7\right)}\)
\(=\dfrac{3}{7}\)
C=\(\frac{1.2.3+2.4.6+4.8.12+7.14.21}{1.3.5+2.6.10+4.12.20+7.21.35}+\frac{74.147-73}{73.147+74}+216,6\)
=\(\frac{2+4+14}{5+10+35}+0+216,6\)
=\(\frac{2+2+2}{5+5+5}+0+216,6\)
=0+0+216,6
=216,6
\(\frac{1.2.3+2.4,6+4.8.12+7.14.21}{1.3.5+2.6.10+4.12.20+7.21.35}\)
\(=\frac{1\left(1.2.3\right)+2\left(1.2.3\right)+4\left(1.2.3\right)+7\left(1.2.3\right)}{1\left(1.3.5\right)+2\left(1.3.5\right)+4\left(1.2.3\right)+7\left(1.2.3\right)}\)
\(=\frac{6\left(1+2+4+7\right)}{15\left(1+2+4+7\right)}=\frac{6}{15}=\frac{3}{5}\)
tính hợp lý \(\frac{9764}{36615}+\frac{36\cdot85\cdot20}{25\cdot84\cdot34}+2\cdot2+3\frac{19}{133}\)
Lời giải:
Gọi giá trị trên là $A$
$A=\frac{4}{15}+\frac{6}{7}+4+3+\frac{1}{7}$
$=\frac{4}{15}+(4+3)+(\frac{6}{7}+\frac{1}{7})$
$=\frac{4}{15}+7+1=8\frac{4}{15}$