Question

(2x + 1) ^ 2 >= 4x ^ 2 - 3 Giải giúp vs ạ

Answer 1

\(\left(2x+1\right)^2\ge4x^2-3\)

\(\Leftrightarrow4x^2+2x+2x+1\ge4x^2-3\)

\(\Leftrightarrow4x^2-4x^2+2x+2x\ge-3-1\)

\(\Leftrightarrow4x\ge-4\\ \Leftrightarrow x\ge-1\)

Vậy phương trình có tập nghiệm là:\(S=\left\{x|x\ge-1\right\}\)

Answer 2

\(\left(2x+1\right)^2\ge4x^2-3\)

\(\Leftrightarrow4x^2+4x+1\ge4x^2-3\)

\(\Leftrightarrow4x^2-4x^2+4x\ge-3-1\)

\(\Leftrightarrow4x\ge-4\)

\(\Leftrightarrow x\ge-1\)

Answer 3

\(\left(2x+1\right)^2\ge4x^2-3\\ \Leftrightarrow4x^2+4x+1-4x^2+3\ge0\\ \Leftrightarrow4x\ge-4\\ \Leftrightarrow x\ge-1\)

Vậy: S= [-1; +∞)