x+6x+9=2
7x=2-9
7x=-7
x=-1
x^2 из корня выходит как x
Правило умножения многочленов: каждый член одного многочлена умножить на каждый член второго, привести подобные слагаемые (если возможно).
1) (a - 5)(11 - b) = 11a - ab - 55 + 5b;
2) (-8 - a)(b + 2) = -8b - 16 - ab - 2a;
3) (-7 - b)(a - 7) = -7a + 49 - ab + 7b;
4) (x - 4)(x + 8) = x² + 8x - 4x - 32 = x² + 4x - 32;
5) (x - 5)(9 - x) = 9x - x² - 45 + 5x = -x² + 14x - 45;
6) (8 + 3x)(2y - 1) = 16y - 8 + 6xy - 3x;
7) (2a - 1)(3a + 7) = 6a² + 14a - 3a - 7 = 6a² + 11a - 7;
8) (3a - 2b)(2a - 3b) = 6a² - 9ab - 4ab + 6b² = 6a² - 13ab + 6b²;
9) (15a + 27)(-5a - 9) = -75a² - 135a - 135a - 243 = -75a² - 270a - 243.
1) (1 - cosα + cos2α)/(sinα - sin2α) = (1 - cosα + 2cos²α - 1)/(sinα - 2sinαcosα) = ( 2cos²α - cosα)/(sinα(1 - 2cosα)) = - cosα(1 - 2cosα)/(sinα(1 - 2cosα)) = - cosα/sinα = -ctgα.
2) sin10°sin30°sin50°sin70° = (2sin10°cos10°sin30°sin50°sin70°)/(2cos10°) = (sin20°sin30°sin50°sin70°)/(2cos10°) = (2sin20°sin30°sin50°cos20°)/(4cos10°) = (sin40°sin30°sin50°)/(4cos10°) = (2sin40°sin30°cos40°)/(8cos10°) = (sin80°sin30°)/(8cos10°) = (cos10°sin30°)/(8cos10°) =(sin30°)/8 = 0,5/8 = 1/16.
3) sinπ/16cos³π/16 - sin³π/16cosπ/16 = sinπ/16cosπ/16(cos²π/16 - sin²π/16) = 0,5·2sinπ/16cosπ/16(cos2π/16) = 0,5sin2π/16cosπ/8 = 0,5sinπ/8cosπ/8 = 0,25·2sinπ/8cosπ/8 = 0,25sin2π/8 = 0,25sinπ/4 = 0,25·√2/2 = √2/8
4) sin(2α - π)/(1 - sin(3π/2 + 2α)) = -sin(2α)/(1 + cos(2α)) = (-2sinαcosα)/(2cos²α) = (-sinα)/(cosα) = -tgα.
5) (2cos²α - sin2α)/(2sin²α - sin2α) = (2cos²α - 2sinαcosα)/(2sin²α - 2sinαcosα) = -(2cosα(sinα - cosα))/(2sinα(sinα - cosα)) = -(cosα)/(sinα) = -ctgα = 4
6) sin36°/sin12° - cos36°/cos12° = (sin36°·cos12° - sin12°·cos36°)/(sin12°·cos12°) = (2sin(36° - 12°))/(2sin12°·cos12°) = (2sin24°)/(sin24°) = 2
7) cos92°·cos2° + 0,5sin4° + 1 = 0,5(cos(92° - 2°) + cos(92° + 2°)) + 0,5sin4° + 1 = 0,5(cos(90°) + cos(94°)) + 0,5sin4° + 1 = 0,5cos94° + 0,5sin4° + 1 = 0,5cos94° + 0,5sin4° + 1 = 0,5(cos94° + sin4°) + 1 = 0,5(-sin4° + sin4°) + 1 = 0 + 1 = 1.
x во 2 степени +6Х+9-2=0 . По теореме виета: Хпервый=1 Хвторой=-7
ответ: 1;-7