405. Чему равны значения выражений: а) x²; -x²; (-x)² при х = -9; 9; -6; 6; −2; 2; б) х³; -x³; (-x)³ при х = -4; 4; -3; 3; -1; 1?

Решение:

а)

1. x = -9 $$x^2 = (-9)^2 = 81$$ $$-x^2 = -(-9)^2 = -81$$ $$(-x)^2 = (-(-9))^2 = 9^2 = 81$$
2. x = 9 $$x^2 = (9)^2 = 81$$ $$-x^2 = -(9)^2 = -81$$ $$(-x)^2 = (-9)^2 = 81$$
3. x = -6 $$x^2 = (-6)^2 = 36$$ $$-x^2 = -(-6)^2 = -36$$ $$(-x)^2 = (-(-6))^2 = (6)^2 = 36$$
4. x = 6 $$x^2 = (6)^2 = 36$$ $$-x^2 = -(6)^2 = -36$$ $$(-x)^2 = (-6)^2 = 36$$
5. x = -2 $$x^2 = (-2)^2 = 4$$ $$-x^2 = -(-2)^2 = -4$$ $$(-x)^2 = (-(-2))^2 = (2)^2 = 4$$
6. x = 2 $$x^2 = (2)^2 = 4$$ $$-x^2 = -(2)^2 = -4$$ $$(-x)^2 = (-2)^2 = 4$$

б)

1. x = -4 $$x^3 = (-4)^3 = -64$$ $$-x^3 = -(-4)^3 = -(-64) = 64$$ $$(-x)^3 = (-(-4))^3 = (4)^3 = 64$$
2. x = 4 $$x^3 = (4)^3 = 64$$ $$-x^3 = -(4)^3 = -64$$ $$(-x)^3 = (-4)^3 = -64$$
3. x = -3 $$x^3 = (-3)^3 = -27$$ $$-x^3 = -(-3)^3 = -(-27) = 27$$ $$(-x)^3 = (-(-3))^3 = (3)^3 = 27$$
4. x = 3 $$x^3 = (3)^3 = 27$$ $$-x^3 = -(3)^3 = -27$$ $$(-x)^3 = (-3)^3 = -27$$
5. x = -1 $$x^3 = (-1)^3 = -1$$ $$-x^3 = -(-1)^3 = -(-1) = 1$$ $$(-x)^3 = (-(-1))^3 = (1)^3 = 1$$
6. x = 1 $$x^3 = (1)^3 = 1$$ $$-x^3 = -(1)^3 = -1$$ $$(-x)^3 = (-1)^3 = -1$$

Ответ: а) 81; -81; 81; 81; -81; 81; 36; -36; 36; 36; -36; 36; 4; -4; 4; 4; -4; 4. б) -64; 64; 64; 64; -64; -64; -27; 27; 27; 27; -27; -27; -1; 1; 1; 1; -1; -1.