Question

Se considera expresia E(x)=x²+x+√2(2√3+1).Calculati valoarea expresiei pentru x=√3-√2..Va rog ,repede!

Answer 1

$E(x)=x^2+x+ \sqrt{2} (2 \sqrt{3} +1) \\ ( \sqrt{3} - \sqrt{2} )^2+ \sqrt{3} - \sqrt{2} + \sqrt{2} (2 \sqrt{3} +1)= \\ = \sqrt{3} ^2-2 \cdot \sqrt{3} \cdot \sqrt{2}+ \sqrt{2} ^2+ \sqrt{3} - \sqrt{2} +2 \sqrt{6} + \sqrt{2} = \\ =3-2 \sqrt{6} +2+ \sqrt{3} - \sqrt{2} +2 \sqrt{6} + \sqrt{2} =5+ \sqrt{3}$