Question 54440
Try this:
Let x be the smaller number, then x+1 will be the next consecutive number.
{{{x^2 + (x+1)^2 = 2x^2+35}}} Simplify and solve for x.
{{{x^2 + (x^2+2x+1) = 2x^2+35}}}
{{{2x^2+2x+1 = 2x^2+35}}} Subtract 2x^2 from both sides.
{{{2x+1 = 35}}} Subtract 1 from both sides.
{{{2x = 34}}} Finally, divide both sides by 2.
{{{x = 17}}} and {{{x+1 = 18}}}

Check:
{{{17^2 + 18^2 = 289 + 324}}} = 613
{{{2(17^2) + 35 = 578 + 35}}} = 613