Câu hỏi
Tính nhanh:
\(a)\ {{56}^{2}}-{{44}^{2}}-{{23}^{2}}+{{77}^{2}}\)
\(b)\ {{103}^{2}}-{{3}^{2}}-100.6\)
\(c)\ {{203}^{2}}-{{103}^{2}}\)
\(d)\ 20,{{5}^{2}}-10,{{5}^{2}}\)
Lời giải chi tiết:
Hướng dẫn chi tiết:
\(\begin{array}{l}a)\;{56^2} - {44^2} - {23^2} + {77^2}\\ = \left( {{{56}^2} - {{44}^2}} \right) - \left( {{{23}^2} - {{77}^2}} \right)\\ = \left( {56 + 44} \right)\left( {56 - 44} \right) - \left( {23 + 77} \right)\left( {23 - 77} \right)\\ = 100.12 - 100.\left( { - 54} \right)\\ = 100\left( {12 + 54} \right)\\ = 100.66 = 6600\end{array}\)
\(\begin{array}{l}b)\;{103^2} - {3^2} - 100.6\\ = \left( {103 - 3} \right)\left( {103 + 3} \right) - 100.6\\ = 100.106 - 100.6\\ = 100\left( {106 - 6} \right)\\ = 100.100 = 10000\end{array}\)
\(\begin{array}{l}c) \;{203^2} - {103^2}\\ = \left( {203 - 103} \right)\left( {203 + 103} \right)\\ = 100.306 = 30600\end{array}\)
\(\begin{array}{l}d)\;20,{5^2} - 10,{5^2}\\ = \left( {20,5 - 10,5} \right)\left( {20,5 + 10,5} \right)\\ = 10.31 = 310\end{array}\)
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