Question

Aflati ca numarul N=2005+2×(1+2+3+…+2004) este patratul unui numar natural

Answer 1

N=2005+2×(1+2+3+…+2004)

N = 2005 + 2 × 2004 × (2004 + 1) : 2

N = 2005 + 2 × 2004 × 2005 : 2

N = 2005 + 2004 × 2005

N = 2005 × (1 + 2004)

N = 2005 × 2005

N = 2005^2 patrat perfect
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Answer 2

N = 2005 + 2 × ( 1 + 2 + 3 + ....... + 2004 )

N = 2005 + 2 × 2004 × ( 1 + 2004 ) : 2

N = 2005 + 2004 × 2005

N = 2005 × ( 1 + 2004 )

N = 2005 × 2005

N = 2005² → patrat perfect