1. = 16x^2-24xy+9y^2 - 6x^2 - 3xy + 10xy + 5y^2 = 10x^2 - 17xy + 16y^2
2. xy^2 (25x^2 - 4y^2) = xy^2 (5x-2y)(5x+2y)
45-30a+5a^2 = 5 (a^2-6a+9) = 5 (a-3)^2
3. 4x^2-9 = 4x^2+4x-1
4x = -8
x=-2
4. 8x+2y=-20
5x-2y=-19
13x=-39
y=-10-4x
x=-3
y=-10-4*(-3) = 2
Ответ: (3,2)
5. a, a+1, a+2, a+3
(a+2)*(a+3)= a*(a+1)+34
a^2+2a+3a+6=a^2+a+34
4a=28
a=7
7, 8, 9, 10
6. x^2+10x+25+y^2+6y+9=0
(x+5)^2+(y+3)^2 = 0
(y+3)^2 = - (x+5)^2
y+3= - x - 5
y= -x - 8
вар. 2.
1. 49a^2+28ab+4b^2 - 12a^2 +4ab -15ab +5b^2 = 37a^2 + 17ab + 9b^2
2. m^2n (36n^2-49m^2) = m^2n (6n-7m)(6n+7m)
3. 9x^2-4 = 9x^2-9x +5
9x=9
x=1
4. 9x-3y=51
2x+3y=-7
11x=44
y=3x-17
x=4
y=3*4-17 = -5
ответ: (4, -5)
5. a, a+1, a+2, a+3
(a+1)*(a+3)=a*(a+2) + 31
a^2 + a + 3a + 3 = a^2 + 2a + 31
2a=28
a=14
14,15,16,17
6. x^2-8x+16 + y^2-12y+36 =0
(x-4)^2 + (y-6)^2 = 0
x- 4 = - (y-6)
x-4 = -y +6
y = - x +10