Phương trình d: \(y=k\left(x-1\right)+1=kx-k+1\)
Phương trình hoành độ giao điểm (C) và (d):
\(\dfrac{2x+4}{1-x}=kx-k+1\)
\(\Leftrightarrow kx^2-\left(2k-3\right)x+k+3=0\)
\(\Delta=\left(2k-3\right)^2-4k\left(k+3\right)=-24k+9\ge0\Rightarrow k\le\dfrac{3}{8}\)
\(\left\{{}\begin{matrix}x_M+x_N=\dfrac{2k-3}{k}\\x_M.x_N=\dfrac{k+3}{k}\end{matrix}\right.\)
\(MN^2=\left(x_M-x_N\right)^2+\left(y_M-y_M\right)^2=90\)
\(\Leftrightarrow\left(k^2+1\right)\left(x_M-x_N\right)^2=90\)
\(\Leftrightarrow\left(k^2+1\right)\left[\left(x_M+x_N\right)^2-4x_Mx_N\right]=90\)
\(\Leftrightarrow\left(k^2+1\right)\left[\dfrac{\left(2k-3\right)^2}{k^2}-\dfrac{4\left(k+3\right)}{k}\right]=90\)
\(\Leftrightarrow\left(k^2+1\right)\left(3-8k\right)=30k^2\)
\(\Leftrightarrow8k^3+27k^2+8k-3=0\)
\(\Leftrightarrow\left(k+3\right)\left(8k^2+3k-1\right)=0\)
\(\Leftrightarrow...\)
Cho cos x + sin x =\(\dfrac{3}{4}\) . Tính giá trị biểu thức A = \(\left|sinx-cosx\right|\)