1)
(x-1)/(y+2)=6/7
7*(x-1)=6*(y+2)
(7*(x-1))²=(6*(y+2))²
49*(x-1)²=36*(y+2)²
2)
(x-1)²+(y+2)²=85/9 |×36
36*(x-1)²+36*(y+2)²=85*36/9
36*(x-1)²+36*(y+2)²=85*4
36*(x-1)²+49*(x-1)²=85*4
85*(x-1)²=85*4 |÷85
(x-1)²=4
x-1=2 x₁=3 ⇒
(3-1)/(y+2)=6/7
y+2=2*(7/6)=7/3=2¹/₃
y₁=1/3.
x-1=-2 x₂=-1 ⇒
(-1-1)/(y+2)=6/7
y+2=-2*7/6=-14/6=-7/3=-2¹/₃
y₂=-4¹/₃.
Ответ: x₁=3 y₁=1/3 x₂=-1 y₂=-4¹/₃.
<span>Д=25+40=65 </span>
<span>х1=(5+корень65)/2 </span>
<span>х2=(5-корень65)/2</span>
А) -5; -4; -3; -2;
б) -1; 1; 2; 3; 4
1) f(x) = x²+3x-2, x₀=-1
f'(x)=2x+3
f'(-1)=2*(-1)+3=-2+3=1
ответ: 1
2) f(x)=sinx-cosx, x₀=pi/2
f'(x)=cosx-(-sinx)=cosx+sinx
f'(pi/2)=cos pi/2+sin pi/2=1+0=1
ответ: 1
3)f(x)=x-√x, x₀=4
f'(x)=1+1/(2√x)
f'(4)=1+1/(2√4)=1+1/(2*2)=1+1/4=5/4=1.25
ответ: 1.25