Question 438870
Let x the smaller number, then 8-x is the greater. Since their squares is 34, we 

get the equation:{{{(8-x)^2+x^2=34}}}, we solve this equation:

{{{64-16x+x^2+x^2-34=0}}} => {{{2x^2-16x+30=0}}}, divide both sides by 2:

{{{x^2-8x+15=0}}}, solving this equation by factoring we have:

{{{(x-5)(x-3)=0}}} x=5 and x=3.

Answer:The smaller number is 3.

Check:{{{3^2+(8-3)^2=34}}} => {{{9+25=34}}} => {{{34=34}}}.