Question

considere os numeros  a= √2+√3 e b = 4-√24.o valor de a^2+b^2 é:

a)3-5√3
 b)42+12√7
c)45-14√6
d)72+13√7
e)9-5√3

Answer 1

$a^2+b^2=( \sqrt{2} + \sqrt{3} )^2+ (4- \sqrt{24})^2=2+3+(4- \sqrt{24})*(4- \sqrt{24})=$
$5+(4^2- 4\sqrt{24}-4\sqrt{24}+24)=5+(16-8\sqrt{24}+24)=$=$45-8\sqrt{24}=45-8\sqrt{2^2*6}=45-8*2\sqrt{6}=45-16\sqrt{6}$