Răspuns
Explicație pas cu pas:
A = 1987 + 2 × ( 1 + 2 + 3 + .... + 1 986 )
A = 1987 + 2 × 1986 × ( 1 + 1986 ) : 2
A = 1 987 + 1986 × 1987
A = 1987 × ( 1 + 1986 )
A = 1987 × 1987
A = 1987² → patrat perfect
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B = 64 + 64 × 2 + 64 × 3 + ...... + 64 × 47
B = 64 × ( 1 + 2 + 3 + ..... + 47 )
B = 64 × 47 × ( 1 + 47 ) : 2
B = 64 × 47 × 24
B = 8² x 47 x 2² x 6 → NU ESTE patrat perfect
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B este patrat perfect daca in loc de 47 este 49
B= 64 + 64 × 2 + 64 × 3 + .... + 64 × 47 + 64 × 48 + 64 × 49
B = 64 × ( 1 + 2 + 3 + ..... + 49 )
B = 64 × 49 × 50 : 2
B = 8² x 7² x 5²
B = ( 8 x 7 x 5)²
B = 280² → patrat perfect
