Question

2x-x²=2

x³+15x²+75x+125=0

x³+48x=12x²+64

Answer 1

\(2x-x^2=2\\ \Leftrightarrow x^2-2x+2=0\\ \Leftrightarrow\left(x^2-2x+1\right)+1=0\\ \Leftrightarrow\left(x-1\right)^2+1=0\\ Mà:\left(x-1\right)^2\ge0\forall x\in R\\ \Rightarrow\left(x-1\right)^2+1\ge1\forall x\in R\\ Vậy:Pt.vô.nghiệm\\ x^3+15x^2+75x+125=0\\ x^3+3.x^2.5+3.x.5^2+5^3=0\\ \left(x+5\right)^3=0\\ \Leftrightarrow x+5=0\\ \Leftrightarrow x=-5\\ x^3+48x=12x^2+64\\ \Leftrightarrow x^3-12x^2+48x-64=0\\ \Leftrightarrow x^3-3.x^2.4+3.x.4^2-4^2=0\\ \Leftrightarrow\left(x-4\right)^3=0\\ \Leftrightarrow x-4=0\\ \Leftrightarrow x=4\)