Question 42404
Let x and y be two consecutive numbers
so we can write y=x+1    ------>(1)
Given:{{{x^2+y^2=85}}}    ---------->(2)
Plugin equation(1) in equation(2)
{{{x^2+(x+1)^2=85}}}
{{{x^2 +x^2+1+2x=85}}}
{{{2x^2+2x+1=85}}}
{{{2x^2+2x-84=0}}}
{{{2(x-6)(x+7)=0}}}
x=6,x=-7
leaving the negative number so we get x=6 
sofrom equation(1) we get  

 y=6+1=7

So the two consecutive numbers are x=6 and y=7

checking: substitute values of  x and y in equation (2)
{{{6^2+7^2=85}}}
{{{36+49=85}}}
{{{85=85}}} that's true!
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