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2(a +b)=28             a+b=14                  a=14-b         

a^2+b^2=100,       a^2+b^2=100,        (14-b)^2+b^2=100,      14^2 -2*14b+b^2+b^2=100

                                                                                                          196-28b+2b^2=100

                                                                                                           2b^2-28b+196-100=0

                                                                                                           2b^2-28b+96=0,   делим на2

                                                                                                           b^2-14b+48=0,      

                                                                                                           D=14^2-4*48

                                                                                                           D=196-192=4

                                                                                                           b=(-(-14)+кв.корень из 4)/2

                                                                                                           b=(14+2)/2

                                                                                                           b=16/2

                                                                                                           b=8

                                                                                  a=14-8=6.

Для другого корня квадрвтного уравнеия:                            b=(14-2)/2

                                                                                                          b=6

                                                                                  a=14-6=8.   Всё!