Question

Знайти значення виразу

Answer 1

$sqrt{aбsqrt{b}}=sqrt{frac{a+sqrt{a^2-b}}{2}}бsqrt{frac{a-sqrt{a^2-b}}{2}}\ ------------------$


$sqrt{43+6sqrt{28}}=sqrt{43+sqrt{36*28}}=sqrt{43+sqrt{1008}}= \ \ =sqrt{frac{43+sqrt{43^2-1008}}{2}}+sqrt{frac{43-sqrt{43^2-1008}}{2}}= \ \ =sqrt{frac{43+sqrt{1849-1008}}{2}}+sqrt{frac{43-sqrt{1849-1008}}{2}}= \ \ =sqrt{frac{43+sqrt{841}}{2}}+sqrt{frac{43-sqrt{841}}{2}}= sqrt{frac{43+29}{2}}+sqrt{frac{43-29}{2}}= \ \ =sqrt{frac{72}{2}}+sqrt{frac{14}{2}}=sqrt{36}+sqrt{7}=6+sqrt{7}$


$sqrt{43-6sqrt{28}}=sqrt{43-sqrt{36*28}}=sqrt{43-sqrt{1008}}= \ \ =sqrt{frac{43+sqrt{43^2-1008}}{2}}-sqrt{frac{43-sqrt{43^2-1008}}{2}}= \ \ =sqrt{frac{43+sqrt{1849-1008}}{2}}-sqrt{frac{43-sqrt{1849-1008}}{2}}= \ \ =sqrt{frac{43+sqrt{841}}{2}}-sqrt{frac{43-sqrt{841}}{2}}= sqrt{frac{43+29}{2}}-sqrt{frac{43-29}{2}}= \ \ =sqrt{frac{72}{2}}-sqrt{frac{14}{2}}=sqrt{36}-sqrt{7}=6-sqrt{7}$


$6+sqrt{7}+6-sqrt{7}=6+6=12$