Question

calculati a si apoi aratati ca este patrat perfect

a= (2 + 4 + 6 + 8 +….
+2012) +1007

a=2*(1+2+3+….+24)+25

a=(3+6+9+12+….+147)+1225

Answer 1

Răspuns:

Explicație pas cu pas:

a = (2+4+6+8+.....+2012) + 1007

a = 2×(1+2+3+4+......+1006) + 1007

a = 2×1006 × (1+1006) : 2 + 1007

a = 1006 × 1007 + 1007

a = 1007 × (1006+1)

a = 1007 × 1007

a = 1007² → pătrat perfect

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a = 2×(1+2+3+......+24) + 25

a = 2×24×(1+24) : 2 + 25

a = 24 × 25 + 25

a = 25 × ( 24 + 1)

a = 25 × 25

a = 25² → pătrat perfect

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a = (3+6+9+12+.....+147) + 1 225

a = 3×(1+2+3+4+.....+49) + 1 225

a = 3 × 49 × (1+49) : 2 + 1 225

a = 147 × 50 : 2 + 1 225

a = 147 × 25 +  25 × 49

a = 25 × (147 + 49)

a = 25 × 196

a = 5² × 14²

a = (5×14)²

a = 70² → pătrat perfect