Răspuns:
1/a) 0^2=0, 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36,7^2=49.
1+4+9+16+25+36+49
=50+40+34+16=90+50=140
b) 0^3+1^3+2^3+3^3+4^3
=1+8+27+64
=65+35=100
2/a) 3^2+3^×7=
=3^2×(5+7)
=9×12
=108
b) 2025^2019-2024×2025^2018=
=2025^2018×(2025^1-2024)
=2025^2018×1
=2025^2018
c) (7^10-7^9):(7^9-7^8)=
=7^9×(7^1-7^0):7^8(7^1-7^0)
=7^9×(7-1):7^8×(7-1)
=7^9×6:7^8×6
=7^1
=7
d) 5^3-2^6-5^3×7^2=
=5^3×(2^6-7^2)
=125×15
=1875
3/ 3^27-27^12=2×81^10:x^2
=3^37-(3^3)^12=2×(3^4)^10:x^2
=3^37-3^36=2×3^40:x^2
=3^36(3-1)=2×3^40:x^2
=2×3^36=2×3^40:x^2
=3^36=3^40:x^2
x^2=3^4
x=3^2
x=9
9/ 100+2×99×100:2=100+99×100=
100(1+99)
N=100×100
Patrat perfect = 100^2
Sunt bine, deoarece le-am avut și eu!
