Question

x⁴+x²+1

Answer 1

ta có: \(x^4+x^2+1\)

\(=\left(x^2\right)^2+2.x^2.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)

\(=\left(x^2+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)

Vì \(\left(x^2+\dfrac{1}{2 }\right)^2\ge0\)

Nên \(\left(x^2+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)

Answer 2

x⁴ + x² + 1 = (x⁴ + 2x² + 1) – x²
= [(x²)² + 2x² + 1] – x²

= [x² + 1]² – x²

= [x2 + 1 + x] [x2 + 1 – x]