b)Đk:\(x\ge-\frac{1}{16}\)
\(\Leftrightarrow-2\sqrt{1+16x}=2-x^2+x\)
Bình 2 vế
\(\left(-2\right)^2\sqrt{\left(1+16x\right)^2}=\left(2-x^2+x\right)^2\)
\(\Leftrightarrow64x+4=x^4-2x^3-3x^2+4x+4\)
\(\Leftrightarrow x^4-2x^3-3x^2-60x=0\)
\(\Leftrightarrow x\left[x^3-2x^2-3x-60\right]=0\)
\(\Leftrightarrow x\left[x^3+3x^2+12x-5x^2-15x-60\right]=0\)
\(\Leftrightarrow x\left[x\left(x^2+3x+12\right)-5\left(x^2+3x+12\right)\right]=0\)
\(\Leftrightarrow x\left[\left(x-5\right)\left(x^2+3x+12\right)\right]=0\)
\(\Leftrightarrow\begin{cases}x=0\left(loai\right)\\x-5=0\\x^2+3x+12=0\end{cases}\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=5\left(tm\right)\\x^2+3x+12=0\left(2\right)\end{array}\right.\)
\(\left(2\right)\Leftrightarrow\left(x+\frac{3}{2}\right)^2+\frac{39}{4}>0\)
->vô nghiệm
Vậy pt trên có nghiệm duy nhất là x=5
Đk:\(x\ge-2010\)
Đặt \(\sqrt{x+2010}=t\left(t\ge0\right)\)
\(pt\Rightarrow x^2+t=t^2-x\)
\(\Rightarrow x^2-t^2+x+t=0\)
\(\Rightarrow\left(x+t\right)\left(x-t+1\right)=0\)
dễ nhé :D
