Question

Aratati ca . A=|rad din5-3|+4/3-rad5 /=supra

Answer 1

A=|√5 - 3| + 4/3-√5
= 3-√5 + 4(3+√5)/(3-√5)(3+√5)  am amplificat fractia cu 3+√5
= 3-√5 + 4(3+√5)/3²-5
= 3-√5 +4(3+√5)/4 simplifici 4 cu 4
= 3-√5 + 3+√5 = 6

Answer 2

    
$\sqrt{5}<3 \\ \\ a=| \sqrt{5} -3|+ \frac{4}{3-\sqrt{5}} = \\ \\= 3-\sqrt{5}+ \frac{4}{3-\sqrt{5}} = \\ \\ = \frac{(3-\sqrt{5})^{2}+4}{3-\sqrt{5}}= \\ \\ \frac{9-6\sqrt{5}+5+4}{3-\sqrt{5}}= \frac{18-6\sqrt{5}}{3-\sqrt{5}}= \frac{6(3-\sqrt{5})}{3-\sqrt{5}}=6$