Question

\(^{\left(x+1\right)^43\left(x^2+2x\right)-3=0}\)

Answer 1

(x+1)^4+3(x^2+2x)-3=0

=>(x^2+2x+1)^2+3(x^2+2x)-3=0

=>(x^2+2x)^2+2(x^2+2x)+3(x^2+2x)+1-3=0

=>(x^2+2x)^2+5(x^2+2x)-2=0

\(\Leftrightarrow x^2+2x=\dfrac{-5+\sqrt{33}}{2}\)

\(\Leftrightarrow2x^2+4x=-5+\sqrt{33}\)

=>\(2x^2+4x+5-\sqrt{33}=0\)

\(\text{Δ}=4^2-4\cdot2\cdot\left(5-\sqrt{33}\right)=16-40+8\sqrt{33}=8\sqrt{33}-24>0\)

=>PT có hai nghiệm pb là:

\(\left\{{}\begin{matrix}x_1=\dfrac{-4-\sqrt{8\sqrt{33}-24}}{4}\\x_2=\dfrac{-4+\sqrt{8\sqrt{33}-24}}{4}\end{matrix}\right.\)