Verified answer

[tex]3 {x}^{2} - 242 = (x + 1) {}^{2} + (x + 2) {}^{2} \\ 3x {}^{2} - 242 = {x}^{2} + 2x + 1 + {x}^{2} + 4x + 4 \\ 3 {x}^{2} - 242 = 2 {x}^{2} + 6x + 5 \\ 3 {x }^{2} - 242 - 2 {x}^{2} - 6x - 5 = 0 \\ {x}^{2} - 6x - 247 = 0 \\ d = ( - 6) {}^{2} - 4 \times 1 \times (- 247) = \\ 36 + 988 = 1024 \\ x _{1} = \frac{6 + 32}{2} = \frac{38}{2} = 19 \\ x _{2} = \frac{6 - 32}{2} = - \frac{26}{2} = - 13[/tex]

1 вариант:

19 ; 20 ; 21

2 вариант:

-13 ; -12 ; - 11

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