2) a*b*b*c*a*c = 18*25*8
a^2*b^2*c^2 = 2*9*25*2*4
abc = 2*2*3*5
корень(abc) = корень(2*2*3*5) = 2*корень (15) - последний вариант
3) a+b = 10 a^2+b^2 = 60
(a+b)^2 = a^2+2ab+b^2 =10^2 = 100
2ab = (a+b)^2 -(a^2+b^2) = 100 -60 =40
ab = 40/2 =20
(a^2+b^2)^2 = a^4+2a^2b^2+b^4
(a^2+b^2)^2 = 60^2 = 3600
2a^2b^2 = 2(ab)^2 = 2*(20)^2 = 2*400 = 800
a^4+b^4 = (a^2+b^2)^2 - 2a^2b^2 = 3600 -800 = 2800
Ответ: 2800
4)
x^2+y^2 = 20
xy = 8
(x+y)^2 = x^2+y^2 + 2xy = 20 + 2*8 = 20+16 = 36
Ответ: 36
5) сложим левые и правые части уравнений
x^3+2x^2y + xy^2 -x - y + y^3 +2xy^2+x^2y +x+y = 2+6
x^3+3x^2y+3xy^2+y^3 =8
(x+y)^3 = 8
x+y = 2
6)
a/b = 2/3 b = 3a/2
c/b = 1/2 b = 2c
2c = 3a/2
c/a =3/(2*2)
c/a = 3/4
7) a^3 +27b^3 = 91 (a+3b)(a^2 - 3ab+9b^2)=91
3ab^2 +a^2b = 28 ab(3b+a) = 28 ab(a+3b)=28 ab = 28/(a+3b)
(a+3b)(a^2 - 3ab+9b^2) 91
---------------------------------- = -----
ab(a+3b) 28
28(a^2 - 3ab+9b^2) = 91ab
28a^2 -84ab+252b^2 -91b = 0
28a^2 - 175ab +252b^2 =0
7(4a^2-25ab+36b^2)=0
7((2a)^2 + 24ab - 24ab -25ab +(6b)^2) = 0
7((2a+6b)^2 - 49ab ) = 0
7((3*(a+3b))^2 - 49ab) =0
7(9(a+3b)^2 - 49ab) =0
9(a+3b)^2 = 49ab
ab = 9(a+3b)^2/49
9(a+3b)^2/49 = 28/(a+3b)
(a+3b)^3 = 28*49/9 = 4*7*7*7/9
a+3b = rкорень кубичный из (4*7*7*7/9) = 7*корень кубичный из (4/9)
8)
x^2+y^2 = 10
xy = 3
(x+y)^2 = x^2+y^2 + 2xy = 10 + 2*3 = 16
9)
пас