Question

Tìm x:

8x³+(x+8)²=8(x+2)(x²-2x+4)

Answer 1

\(8x^3+\left(x+8\right)^2=8\left(x+2\right)\left(x^2-2x+4\right)\)

\(\Leftrightarrow8x^3+x^2+16x+64=8\left(x^3+8\right)\)

\(\Leftrightarrow8x^3+x^2+16x+64=8x^3+64\)

\(\Leftrightarrow8x^3+x^2+16x+64-8x^3-64=0\)

\(\Leftrightarrow x^2+16x=0\)

\(\Leftrightarrow x\left(x+16\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x+16=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=-16\end{array}\right.\)

Answer 2

\(8x^3+\left(x+8\right)^2=8\left(x+2\right)\left(x^2-2x+4\right)\)
\(\Leftrightarrow8x^3+\left(x^2+16x+61\right)=8\left(x^3+2^3\right)\)
\(\Leftrightarrow8x^3+x^2+16x+61=8x^3+61\)
\(\Leftrightarrow8x^3+x^2+16x+61-8x^3-61=0\)
\(\Leftrightarrow x^2+16x=0\)
\(\Leftrightarrow x\left(x+16\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x+16=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=-16\end{array}\right.\)
\(\text{Vậy x=0 hoặc x=-16 }\)