4<span>√3x-<span>√4*3x-<span>√25*3x= 4<span>√3x-2<span>√3x-10<span>√3x=-8<span>√3x</span></span></span></span></span></span></span>
<span><span><span><span><span><span><span>3<span>√4*3+2<span>√3-2<span>√9*3=3*2<span>√3+2<span>√3-2*3<span>√3=6<span>√2+2<span>√3-6<span>√3=2<span>√3</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>(<span>√4*2-<span>√4*6)*<span>√2=(2<span>√2-2<span>√6)*<span>√2=2*2-2<span>√6*2=4-2<span>√12=4-4<span>√3</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>√18*3-<span>√8*3+<span>√50*3=<span>√9*2*3-4<span>√3+<span>√25*2*3=3<span>√6-4<span>√3+5<span>√6=8<span>√6-4<span>√3</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>√16*3-2<span>√3(2-5<span>√3*4)=4<span>√3-2<span>√3(2-10<span>√3)=4<span>√3-4<span>√3+20*3=60</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>
1) 3x²-12x= 3х(х-4)
2) ab-2a+b²-2b=а(b-2)+b(b-2) = = (a+b)(b-2)
3) 4x²-9= (2x-3)(2x+3)
4) x³-8x²+16x=x(x²-8x+16) =x(x-4)²
11.1
(x-3)/(x-1)+(x+3)/(x+1) = (x+6)/(x+2)+(x-6)/(x-2)
Приводим к общему знаменателю слева и справа
((x-3)(x+1)+(x+3)(x-1)) / ((x-1)(x+1)) = ((x+6)(x-2)+(x-6)(x+2))/((x+2)(x-2))
Раскрываем скобки
(x^2-3x+x-3+x^2+3x-x-3) / (x^2-1) = (x^2+6x-2x-12+x^2-6x+2x-12) / (x^2-4)
Приводим подобные
(2x^2 - 6)/(x^2 - 1) = (2x^2 - 24)/(x^2 - 4)
Делим на 2 числители слева и справа
(x^2 - 3)/(x^2 - 1) = (x^2 - 12)/(x^2 - 4)
Применяем пропорцию
(x^2 - 3)(x^2 - 4) = (x^2 - 12)(x^2 - 1)
Замена x^2-3 = y, тогда x^2-4 = y-1; x^2-12 = y-9; x^2-1 = y+2
y(y - 1) = (y - 9)(y + 2)
y^2 - y = y^2 - 9y + 2y - 18
Переносим 18 влево, а все у вправо
18 = -6y
y = -3 = x^2 - 3
x^2 = 0; x = 0
11.2.
ax^2/(x-1) = (a+1)^2
Умножаем все на (x-1)
ax^2 = (x-1)(a+1)^2 = x(a+1)^2 - (a+1)^2
Переносим влево
ax^2 - x(a+1)^2 + (a+1)^2 = 0
Получили квадратное уравнение
D = b^2 - 4ac = (a+1)^4 - 4a(a+1)^2 = (a+1)^2*((a+1)^2 - 4a) =
= (a+1)^2*(a^2+2a+1-4a) = (a+1)^2*(a^2-2a+1) = (a+1)^2*(a-1)^2
x1 = (-b - √D)/(2a) = ((a+1)^2 - (a+1)(a-1))/(2a) =
= (a^2+2a+1-a^2+1)/(2a) = (2a+2)/(2a) = (a+1)/a
x2 = (-b + √D)/(2a) = ((a+1)^2 + (a+1)(a-1))/(2a) =
= (a^2+2a+1+a^2-1)/(2a) = (2a^2+2a)/(2a) = a+1
Решение
1) 9a² - 16b² = (3a - 4b)*(3a + 4b)
2) - 5x + 10x - 5 = - 5*(x² - 10x + 1) = - 5*(x - 1)² = - 5*(x - 1)*(x - 1)
2)5+x²-(x+1)(x+6)=5+x²-(x²+6x+x+6)=5+x²-x²-6x-x-6=-7x-1
при x=0.2
-7*0.2-1=-1.4-1=-2.4
Ответ:-2,4