\(B=\sqrt{x^3+2\left(1+\sqrt{x^3+1}\right)}+\sqrt{x^3+2\left(1-\sqrt{x^3+1}\right)}\)
\(=\sqrt{x^3+1+2\sqrt{x^3+1}+1}+\sqrt{x^3+1-2\sqrt{x^3+1}+1}\)
\(=\sqrt{\left(\sqrt{x^3+1}+1\right)^2}+\sqrt{\left(\sqrt{x^3+1}-1\right)^2}\)
\(=\left|\sqrt{x^3+1}+1\right|+\left|\sqrt{x^3+1}-1\right|\)
\(=\left|\sqrt{x^3+1}+1\right|+\left|1-\sqrt{x^3+1}\right|\)
Áp dụng bđt \(\left|A\right|+\left|B\right|\ge\left|A+B\right|\) ta có:\(B\ge2\)
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