Question

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Answer 1

\(A=\frac{x^3-27}{x-3}+5x=\frac{\left(x-3\right)\left(x^2+3x+9\right)}{x-3}+5x=x^2+8x+9\)

\(=\left(x^2+8x+16\right)-7=\left(x+4\right)^2-7\ge-7\)

=> Min A = -7 <=> x = -4

Answer 2

\(A=\frac{x^3-27}{x-3}+5x=\frac{\left(x-3\right)\left(x^2+3x+9\right)}{x-3}+5x=x^2+3x+9+5x\)

\(=x^2+8x+9=x^2+8x+16-7=\left(x+4\right)^2-7\ge-7\)

Vậy GTNN của A là -7 khi x=-4