Răspuns:
Salutare!
Exercitiul 1:
a) [tex]1^{2}+2^{2}+3^{3}+4^{2} +5^{2}+6^{2} +7^{2}=1+4+9+16+25+36+49=140 [/tex]
b) [tex]1^{3}+2^{3}+3^{3}+4^{3}=1+8+27+64=100[/tex]
Exercitiul 2:
a)[tex]3^{2} X 5+3^{2} X 7= 5 X 3^{2}+7 X 3^{2} = 12 X 3^{2}= 12X9=108 [/tex]
b) [tex]2025^{2019}- 2024 X 2025^{2018} = (2025-2024) X 2025^{2018}= 1 X 2025^{2018}= 2025^{2018} [/tex]
c) [tex](7^{10} - 7^{29}) : (7^{9}-7^{8})= (7-1) X 7^{9}: (7^{9} -7^{8})=6X 7^{9} : [(7-1)X 7^{8}]=6X 7^{9} : (6X 7^{8})= 7 [/tex]
d) [tex]5^{2} X 2^{6} -5^{3} X 7^{2} = (2^{6}- 7^{2} )X 5^{3}= (64-49) X 125= 15X125=1875 [/tex]
Exercitiul 3:
[tex]3^{37} -27^{12} =2 X 81^{10} : x^{2} \\
3^{37} - 3^{36} = \frac{2X 81^{10} }{x^{2} } \\
(3-1) X 3^{36} =\frac{2 X 81^{10}}{x^{2}} \\
2X 3^{36}= \frac{2 X 81^{10}}{x^{2}} \\
2X 3^{36} x^{2} = 2X 81^{10}\\
x^{2} = \frac{81^{10} }{3^{36} } \\
x^{2} =\frac{3^{40} }{3^{36} } \\
x^{2} =3^{4} \\
x^{2} =81\\
x= +- 9\\
x_{1} = -9\\
x_{2}= 9 [/tex]
Explicație pas cu pas:
X- inseamna ori/ inmultit
:- impartit
