y=x^2+4 <span>
x+y=6
</span><span>y=x^2+4
</span>у= 6-х
х^2+4 = 6 - x
x^2 + x+4 - 6 = 0
x^2+x - 2 = 0
D= 1 +8= 9
x₁= -1+3/2 = 1
х₂= -1-3/2 =- 2
у₁= 5
у₂= 8
Ответ: (1;5) и (-2;8).
Уравнение касательной:
y = f(x0) + f'(x0)*(x - x0)
f(x0) = f(-1) = 2*(-1)^2 + 1 = 3
f'(x) = 2*2x + 0 = 4x
f'(x0) = 4*(-1) = -4
y = 3 - 4*(x + 1) = 3 - 4x - 4 = -4x - 1