sự tương giao của đồ thị hàm số

P

perfectday8

$ (d): 0 = -k + b \leftrightarrow b = k \rightarrow (d): y = k(x+1) \\
(C): y = (x+1)(x-2)^2 \\
(C) = (d) \leftrightarrow (x+1)[(x-2)^2-k] = 0 \leftrightarrow x = -1 \vee x = 2 \pm \sqrt{k} \\
A(-1,0) \\ B(2+ \sqrt{k}, 3k+ k \sqrt{k}) \\ C(2- \sqrt{k}, 3k- k \sqrt{k}) \\
BC = \sqrt{(x_B - x_C)^2 + (y_B - y_C)^2} = \sqrt{4k + 4k^3} = 2 \sqrt{k(k^2+1)} \\
h_{\triangle OBC} = d(kx - y + k = 0, O) = \frac{|kx_0 - y_0 + k|}{ \sqrt{k^2 + 1}} = \frac{k}{ \sqrt{k^2 + 1}} \\
S_{\triangle OBC} = \frac{h \times BC}{2} = k \sqrt{k} = 1 \\ \leftrightarrow k = 1. $
 
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