Question

(x−1)(x 2 +x+1)−x(x 2 −1)=7;

Answer 1

$(x - 1)( {x}^{2} + x + 1) - x( {x}^{2} - 1) = 7 \\ {x}^{3} + {x}^{2} + x - {x}^{2} - x - 1 - {x}^{3} + x = 7 \\ x - 1 = 7 \\ x = 8$

Ответ: 8

Answer 2

To solve the equation, let's simplify the expression on the left side and then solve for x:

(x - 1)(x^2 + x + 1) - x(x^2 - 1) = 7

Expanding the expressions within the parentheses:

(x^3 + x^2 + x - x^2 - x - 1) - (x^3 - x) = 7

Simplifying further:

x^3 + x^2 + x - x^2 - x - 1 - x^3 + x = 7

Canceling out like terms:

(1 - 1) + (x^3 - x^3) + (x^2 - x^2) + (x - x) = 7

0 + 0 + 0 + 0 = 7

0 = 7

The equation 0 = 7 is not true. Therefore, the original equation has no solution.