Question

Efectuati:
a)(7√3 + √2) la patrat - 2(1+7√6)=
b)2√5(√3-1) + (√5 -√3) la patrat=
c)12√75 + (6-5√3) la patrat=
d)(3√7 - 2√6) la patrat + 60√126 : (5√3)=
va rooog mult <3

Answer 1

$a).(7 \sqrt{3} + \sqrt{2} )^2-2(1+7 \sqrt{6} ) = \\ \\ =(7 \sqrt{3} )^2+2*7 \sqrt{3} * \sqrt{2} + \sqrt{2} ^2-2-14 \sqrt{6} = \\ \\ =147+14 \sqrt{6} +2-2-14 \sqrt{6} =147+2-2=147 \\ \\ b).2 \sqrt{5} ( \sqrt{3} -1)+( \sqrt{5} - \sqrt{3} )^2= \\ \\ =2 \sqrt{15} -2 \sqrt{5} + \sqrt{5} ^2-2* \sqrt{5} * \sqrt{3} + \sqrt{3} ^2= \\ \\ 2 \sqrt{15} -2 \sqrt{5} +5-2 \sqrt{15} +3=-2 \sqrt{5} +8$

$c).12 \sqrt{75} +(6-5 \sqrt{3} )^2=12*5 \sqrt{3} +6^2-2*6*5 \sqrt{3} +(5 \sqrt{3} )^2= \\ \\ =60 \sqrt{3} +36-60 \sqrt{3} +75=36+75=111 \\ \\ d).(3 \sqrt{7} -2 \sqrt{7} )^2+60 \sqrt{126} :(5 \sqrt{3} )= \\ \\ =(3 \sqrt{7} )^2-2*3 \sqrt{7} *2 \sqrt{7} +(2 \sqrt{7} )^2+12 \sqrt{42} = \\ \\ =63-84+28+12 \sqrt{42} =7+12 \sqrt{42}$