Question

Efectuati:
a)($\sqrt{3}$ - 1) la patrat + $\sqrt{12}$=
b)($\sqrt{5} - \sqrt{3}$) la patrat + 2$\sqrt{5}$ ori $\sqrt{27}$=
c)2($\sqrt{7}$+ 1) la patrat - 2$\sqrt{7}$ - 2) la patrat=
d)($\sqrt{8} - \sqrt{3}$) la patrat + ($\sqrt{6}$ - 1)($\sqrt{6}$ + 1)=

Answer 1

$a).( \sqrt{3} -1)^2+ \sqrt{12} = \sqrt{3} ^2-2* \sqrt{3} *1+1^2+2 \sqrt{3}= \\ \\ =3-2 \sqrt{3} +1+2 \sqrt{3} =3+1=4 \\ \\ b).( \sqrt{5} - \sqrt{3} )^2+2 \sqrt{5} * \sqrt{27} = \sqrt{5} ^2-2* \sqrt{5} * \sqrt{3} + \sqrt{3} ^2+2 \sqrt{5} *3 \sqrt{3} = \\ \\ =5-2 \sqrt{15} +3+6 \sqrt{15} =8+4 \sqrt{15}$

$c).2( \sqrt{7} +1)^2-(2 \sqrt{7} -2)^2= \\ \\ =2( \sqrt{7} ^2+2* \sqrt{7} *1+1^2)-[(2 \sqrt{7} )^2-2*2 \sqrt{7} *2+2^2]= \\ \\ =2(7+2 \sqrt{7} +1)-(28-8 \sqrt{7} +4)= \\ \\ =14+4 \sqrt{7} +2-28+8 \sqrt{7} -4=-16+12 \sqrt{7}$

$d).( \sqrt{8} - \sqrt{3} )^2+( \sqrt{6} -1)( \sqrt{6} +1)=(2 \sqrt{2} - \sqrt{3} )^2+6-1= \\ \\ =(2 \sqrt{2} )^2-2*2 \sqrt{2} * \sqrt{3} + \sqrt{3} ^2+6-1= \\ \\ =8-4 \sqrt{6} +3+6-1=16-4 \sqrt{6}$