Question

Demonstrati identitatea:
$\sqrt{t ^{4}+2t ^{2}+1 } =t ^{2} +1$

Answer 1

$\sqrt{t^4+2t^2+1}= \sqrt{(t^2)^2+2 \cdot t^2 \cdot 1+1^2}= \sqrt{(t^2+1)^2}=|t^2+1|=t^2+1 \\ \\ |t^2+1|=t^2+1~deoarece~t^2 \geq 0,~si,~deci,~t^2+1 \geq 1.$