Question

Вычислите:
$\frac{ {47}^{2} - {3}^{2} }{ {27}^{2} + 2 \times 27 \times 13 + {13}^{2} }$
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Answer 1

Ответ:

$\dfrac{47^2-3^2}{27^2+2\cdot 27\cdot 13+13^2}=\dfrac{(47-3)(47+3)}{(27+13)^2}=\dfrac{44\cdot 50}{40^2}=\dfrac{(4\cdot 11)\cdot (2\cdot 25)}{(4\cdot 10)^2}=\\\\\\=\dfrac{(4\cdot 11)\cdot (2\cdot 25)}{(4\cdot 2\cdot 5)^2}=\dfrac{4\cdot 11\cdot 2\cdot 5^2}{4^2\cdot 2^2\cdot 5^2}=\dfrac{11}{4\cdot 2}=\dfrac{11}{8}=1\dfrac{3}{8}$