Прошу решите задания с фото

(x+2)^3 + (2x-1)(4x^2+2x+1) - 6*(x+1)(x-1) - 9x^3 =
= (x+2)^3 + (2x-1)(4x^2+2x+1) - 6*(x+1)(x-1) - 9x^3 =
= (x^3 + 6x^2 + 12x + 8) + (8x^3 - 1) - 6*(x^2 - 1) - 9x^3 =
= (x^3 + 8x^3 - 9x^3) + (6x^2 - 6x^2) + (12x) + (8 - 1 + 6) =
= 12x + 13 =
= 12 * 1/4 + 13 = 16

4*(a+2b)^2 - 9*(2a+b)^2 =
= {2*(a+2b)}^2 - {3*(2a+b)}^2 =
= (2a+4b)^2 - (6a+3b)^2 =
= [(2a+4b) + (6a+3b)] * [(2a+4b) - (6a+3b)] =
= (8a + 7b) * (-4a+b) =
= -32a - 28ab + 8ab + 7b^2 =
= -32a - 20ab + 7b^2

(x+1)^3 = x^2 * (x+1)
(x+1)^3 - x^2 * (x+1) = 0
(x+1) * [(x+1)^2 - x^2] = 0
(x+1) * (x^2 + 2x + 1 - x^2) = 0
(x+1) * (2x+1) = 0
(x+1) = 0 ---> x1 = 0
(2x+1) = 0 ---> x2 = - 1/2

P = a^2 + 6ab + 10b^2 - 2b + 3 =
= (a^2 + 2*3ab + 9b^2) + (b^2 - 2b + 1) + 2 =
= (a+3b)^2 + (b-1)^2 + 2
(a+3b)^2 >= 0 при любых а и b
(b-1)^2 >= 0 при любых b
=>
P = 0 + 0 + 2 = 2 - минимальное значение

(53^2 - 31^2 - 43^2 + 41^2) / (73^2 - 2*73*63 + 63^2) =
= [(53^2 - 43^2) + (41^2 - 31^2)] / (73 - 63)^2 =
= [(53+43)(53-43) + (41+31)(41-31)] / 10^2 =
= (96*10 + 72*10) / 10^2 =
= 10 * (96+72) / 10*10 =
= 168/10 = 16,8