Question

aratati ca urmatoarele nr sunt pătrate perfecte:a)A=1+2+...+9+1+2+...+9+1+2+....+9+9 și b)B=10^21+2^20×5^21+2^21×5^20+2^23×5^20​

Answer 1

Explicație pas cu pas:

b)

$B = {10}^{21} + {2}^{20} \times {5}^{21} + {2}^{21} \times {5}^{20} + {2}^{23} \times {5}^{20} = 10 \times {10}^{20} + {2}^{20} \times 5 \times {5}^{20} + 2 \times {2}^{20} \times {5}^{20} + {2}^{3} \times {2}^{20} \times {5}^{20} = 10 \times {10}^{20} + 5 \times {10}^{20} + 2 \times {10}^{20} + 8\times {10}^{20} = {10}^{20} \times (10 + 5 + 2 + 8) = {10}^{20} \times 25 = {10}^{20} \times {5}^{2} = \red{\bf {(5 \times {10}^{10}) }^{2}}$