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1)  n + n² = 380

   n² + n - 380 = 0

   Δ = 1 - 4 ( 1 * - 380 ) = 1 + 1 520 = 1 521  = 39 ²

   x ₁  = ( - 1 - 39 ) / 2 = - 40 /2 = - 20

   x ₂ = ( - 1 + 39 ) / 2 = 38/2 = 19

19 + 361   = 380

( - 20 ) + 400 =  380

n ² + ( n + 1 )² + ( n + 2 )² = 1 877

n² + n²  + 2 n + 1 + n² + 4 n + 4 = 1 877

3 n² + 6 n + 5 = 1 877

3 n² + 6 n + 5 - 1 877 = 0

3 n² + 6 n - 1 872 = 0

Δ = 36 - 4 ( 3 * - 1 872 ) = 36 + 22 464 = 22 500  = 150 ²

x ₁ = ( - 6 - 150 ) / 6 = - 156/6 = - 26

x ₂ = ( - 6 + 150 ) / 6  = 144 /6 = 24