5x^2+5x-15=2x^2+11x+9
5x^2-2x^2+5x-11x-15-9=0
3x^2-6x-24=0 |:3
x^2-2x-8=0
по т. Виета:
x1+x2=2
x1*x2=-8
x1=4; x2=-2
Cosα-cosβ= -2sin (α+β)/2 * cos (a-β)/2 Формула суммы косинуса
Подставляем:
-2sin(12+6)/2 * cos(12-6)/2 = -2sin9a*cos3a
№4<span>
1)xy+x/x-y:(y+1)/x+y=x(y+1)</span>×(x+y)/(x-y)×(y+1)x²=x+y/x²-xy
<span>2)x+y/x</span>²-xy×x²-xy/x+y=0
Решение
<span>5^(2х+1) - 26*(5^х) + 5 = 0
5^x = t
5t</span>² - 26t + 5 = 0
D = 676 - 4*5*5 = 576
t₁ = (26 - 24)/10 = 1/5
t₂ = <span>(26 + 24)/10 = 5
1) 5^x = 1/5
5^x = 5</span>⁻¹
x₁ = - 1
2) 5^x = 5
x₂ = 1
Ответ: x₁ = - 1; <span>x₂ = 1</span>
у=1/2+1/2x-2y
3-2x+2-8x=1/5
5-8x=1/5
24/5=8x
x=3/5