Question

Giải phương trình:

\(\left(\dfrac{z^2+2z+4}{z-2}\right)^2+7=\dfrac{8-z^3}{\left(z-2\right)^2}\)

Answer 1

ĐKXĐ: \(z\ne2\)

\(\left(\dfrac{z^2+2z+4}{z-2}\right)^2+7+\dfrac{\left(z-2\right)\left(z^2+2x+4\right)}{\left(z-2\right)^2}=0\)

\(\Leftrightarrow\left(\dfrac{z^2+2z+4}{z-2}\right)^2+\dfrac{z^2-2z+4}{z-2}+7=0\)

Đặt \(\dfrac{z^2+2z+4}{z-2}=x\)

\(\Rightarrow x^2+x+7=0\)

\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{27}{4}=0\)

Pt đã cho vô nghiệm