д) (u+v)(u-v)(u-v)
е) (u +v)(u^2 -uv+v^2)(u+v)
2) а) 1/х1 +1/х2 = (х2 +х1)/х1*х2 по теореме Виета х2+х1= -1/6 х1*х2 = -2/6, значит
1/х1 +1/х2 = (-1/6): (-2/6)= 1/2=0,5
в) (х1^3 +x2 ^3)/(x1 ^3 * x2^3) = (x1+x2)(x1^2 -x1*x2 +x2^2)/(x1*x2)^3 = (x1+x2)(x1^2 -x1*x2 +x2^2 -2x1*x2+2x1*x2)/(x1*x2)^3 = (x1+x2)((x1 +x2)^2 -3x1x2)/(x1*x2)^3 = -1/6 * (1/36 +2/3)/ (-8/216) = -1/6 *25/36 /(-8/216) = -25/216 *(-216/8) = 25/8
б) (-1/6)^2 - 2* (-2/6))^2 - 2*(-2/6)^2 = (1/36 +4/6)^2 - 4/18 = 625/1296 - 4/18 =337/1296
Разложите на множители выражение
(х+у)^2 - ( x^4- 2*x^2*y^2+ y^4 )=
=(х+у)^2 - ( x^2- y^2 )^2=
=(х+у)^2 - ( (x- y) (x+y) )^2=
=(х+у)^2 - (x- y)^2 (x+y)^2=
=(х+у)^2 (1 - (x- y)^2) =
=(х+у)^2 (1 - (x- y)) (1 +(x-y)) =
=(х+у)^2 (1 - x+ y) (1 +x-y)
Сократите дроби:
10а^2-6a+5ab-3b / 5a^2-8a+3=
=2a(5а-3)+b(5a-3) / 5a^2-5a-3a+3=
=(2a+b)(5a-3) / 5a(a-1)-3(a-1)=
=(2a+b)(5a-3) / (a-1)(5a-3)=
=(2a+b) / (a-1)
x^2-4x+1 / x^2-2(2+√3)x+(4+4√3+3)=
=x^2-4x+4-3 / x^2-2(2+√3)x+(2^2+4√3+√3^2)=
=(x-2)^2 - √3^2 / x^2-2(2+√3)x+(2+√3)^2=
=(x-2-√3) (x-2+√3) / ( x - (2+√3) )^2=
=(x-2-√3) (x-2+√3) / ( x- 2-√3)^2 =
=(x-2-√3) (x-2+√3) / ( x-2-√3) (x-2-√3)=
=(x-2+√3) / ( x-2-√3) или =(x+√3-2) / ( x-√3-2)