А) у^2 + 6у + 9 = y^2 + 2•3•y + 3^2 = (y+3)^2
б) 36х^2 -12ху + у^2 = (6х)^2 - 2•6ху + у^2 =
= (6х-у)^2
в) m^2 + 2mn + n^2 = (m+n)^2
г) a²-2ab+b² = (a-b)^2
д) y²-36 = (y^2 - 6^2) = (y+6)(y-6)
е) x²-0,16y² = x^2 - (0,4y)^2 = (x+0,4y)(x-0,4y)
ё) a^6-25 = (a^3)^2 - 5^2 = (a^3 + 5)(a^3 - 5)
ж) 400-y² = 20^2 - y^2 = (20+y)(20-y)
1) рассчитываем диагональ по теореме Пифагора:
√b²+b²= b√2
2) квадрат данной диагонали будет 2b²
3) 1632<2b²<50
(x-1)(x-3)(x+5)(x+7)=297((x – 1)(x + 5))((x – 3)(x + 7)) = 297;(x2 + 5x – x – 5)(x2 + 7x – 3x – 21) = 297;(x2 + 4x – 5)(x2 + 4x – 21) = 297.x2 + 4x = t, тогда :(t – 5)(t – 21) = 297.t2 – 21t – 5t + 105 = 297;t2 – 26t – 192 =0<span>t1=-6 и t2=32</span>x2 + 4x = -6 или x2 + 4x = 32x2 + 4x + 6 = 0 x2 + 4x – 32 = 0D = 16 – 24 < 0 D = 16 + 128 > 0 Нет корней x1 = -8; x2 = 4<span>Ответ: x1=-8 , x2=4</span>