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Arãtati ca numarul b=2•(1+2+3+•••+124)+125 este cub perfect

Răspuns :

b = 2(1+2+...+124) + 125
= 2 * 124 * 125 : 2 + 125
= 124*125 + 125
= 125(124+1)
= 125*125
[tex]=125^2[/tex]
[tex]=(5^3)^2[/tex]
[tex]=(5^2)^3[/tex]
2*124*125/2 +125= 124*125+125= 125(124+1)= 125*125= 5³ * 5³=5^6=
5^(2*3)=(5²)³ =25³, cub perfect