inequality

[kanali]

Prove that for all \(\displaystyle x\geq 1\Longrightarrow x^4-4x+3\geq 0\)

Any ideas how to start?

 

[galactus]

Did you try factoring the given quartic?.

\(\displaystyle (x-1)^{2}(x^{2}+2x+3)\)

 

[BigGlenntheHeavy]

\(\displaystyle One \ way, \ to \ wit: \ x^4-4x+3 \ = \ (x-1)^2(x^2+2x+3) \ and \ x-1 \ \ge \ 0.\)

 

[kanali]

Did you try factoring the given quartic?.

\(\displaystyle (x-1)^{2}(x^{2}+2x+3)\)

Thanks i get it now