1) 2x² + 7x - 9 = 0
D = 7² - 4 * 2 * (- 9) = 49 + 72 = 121 = 11²
2) 100x² - 16 = 0
(10x - 4)(10x + 4) = 0
10x - 4 = 0 10x + 4 = 0
10x = 4 10x = - 4
x₁ = 0,4 x₂ = - 0,4
X² -7x -7x -16 +x² =0
2x² -14x -16 =0
D =14² -4*2*(-16) =196+128 =324 =18²
x1 =(14 -18)/4 = (-1)
x2 =(14+18)/4 =8
ответ: x = -1; x =8
a) tg a ctg a - sin^2 a = 1 - sin^2 a = cos^2 a
б) (cos^2a-1)/cos^2a = -sin^2 a / cos^2 a = - tg^2 a (скобки поставил за автора. Если не так, то уточните условие)
(x^2-1)(x^4+x^2+1)-(x^2-1)(x^2-1)(x^2-1)=(x-1)(x+1)(x^2-x+1)*(x^2+x+1)-(x-1)(x+1)(x-1)^2*(x+1)^2=3x^4-3x^2=3x^2(x-1)(x+1)