Question

(х-1)(х^2+х+1)=999

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Answer 1

$(a - b)(a {}^{2} + 2ab + b {}^{2} ) = a {}^{3} - b {}^{3} \\$

$(x - 1)(x {}^{2} + x + 1) = x {}^{3} - 1$

$x {}^{3} - 1 = 999 \\ x {}^{3} = 999 + 1 \\ x {}^{3} = 1000 \\ x = 10$

Answer 2

(х - 1) (х² + х + 1) = 999;

x × x² + x × x + x × 1 + (- 1) × x² + (- 1) × x + (- 1) × 1 = 999;

x³ + x² + x + (- x²) + (- x) + (- 1) = 999;

x³ + x² + x - x² - x - 1 = 999;

x³ + (x² - x²) + (x - x) - 1 = 999;

x³ + 0 + 0 - 1 = 999;

x³ - 1 = 999;

x³ = 999 + 1;

x³ = 1 000;

x = ∛1 000;

x = ∛10³;

x = 10.

ответ: 10.

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