Question

Помогите пожалуйста !!! см. фото

Answer 1

а)
${46}^{2} - 92 \times 31 + {31}^{2} = {46}^{2} - 2 \times 46 \times 31 + {31}^{2} = {(46 - 31)}^{2} = {15}^{2} = 225$
b)
$\frac{ {37}^{2} - {23}^{2} }{ {47}^{2} - 169 } = \frac{ {37}^{2} - {23}^{2} }{ {47}^{2} - {13}^{2} } = \frac{(37 - 23)(37 + 23)}{(47 - 13)(47 + 13)} = \frac{14 \times 60}{34 \times 60} = \frac{7}{17}$
c)
$\frac{ {26}^{3} + {17}^{3} }{ {26}^{2} - 26 \times 17 + {17}^{2} } = \frac{(2 6 + 17)( {26}^{2} - 26 \times 17 + {17}^{2} )}{ {26}^{2} - 26 \times 17 + {17}^{2} } = 26 + 17 = 43$
d)
$\frac{ {45}^{3} - {25}^{3} }{20} + 45 \times 25 = \frac{(45 - 25)( {45}^{2} + 45 \times 25 + {25}^{2}) }{20} + 45 \times 25 = \frac{20( {45}^{2} + 45 \times 25 + {25}^{2}) }{20} + 45 \times 25 = {45}^{2} + 45 \times 25 + {25}^{2} + 45 \times 25 = {45}^{2} + 2 \times 4 5\times 25 + {25}^{2} = {(45 + 25)}^{2} = {70}^{2} = 4900$
e)
$\frac{ {49}^{2} + {22}^{2} - {29}^{2} - {2}^{2} }{ {65}^{2} - 130 \times 45 + {45}^{2} } = \frac{(49 - 29)(49 + 29) + (22 - 2)(22 + 2)}{ {65}^{2} - 2 \times 65 \times 45 + {45}^{2} } = \frac{20 \times 78 + 20 \times 24}{ {(65 - 45)}^{2} } = \frac{20(78 + 24)}{ {20}^{2} } = \frac{102}{20} = \frac{51}{10} = 5 \frac{1}{10}$