Question 731033
1) {{{a+b=17}}} &  2) {{{a^2+b^2=145}}}

Try to make equation #(2) from equation #(1):

so,  {{{a+b=17}}}  >>> {{{(a+b)^2=17^2}}} >>> {{{(a^2+b^2+2ab)=289}}} >>> from eq. #(2) >>>   {{{(145+2ab)=289}}}  >>> {{{(2ab)=144}}} >>> {{{(ab)=72}}}

Now use these two new equations: (2) {{{a+b=17}}} (3) {{{(ab)=72}}}

 {{{a+b=17}}} >>>   {{{b=17-a}}} substitute in eq. #(3)

 {{{(ab)=72}}} >>> {{{(a(17-a))=72}}} >>> {{{a^2-17a+72=0}}}

{{{(a-8)(a-9)=0}}}  >>> 

(1) {{{a=8}}} >>> {{{b=9}}}  or the other way,
(2) {{{a=9}}} >>> {{{b=8}}}