Question 5743
let x = first whole number
let x+1 = second whole number (because they are consecutive, one number is 1 unit greater than the other)
{{{x^2+(x+1)^2=145}}}
{{{x^2+x^2+2x+1-145=0}}}
{{{2x^2+2x-144=0}}}
{{{x^2 + x -72=0}}}
{{{(x+9)(x-8)}}}
x=-9 or x=8
we can rule out -9, because it is not a whole number
so our first number is 8 and the second number is 9

verify:

{{{8^2+9^2=145}}}
{{{64+81=145}}}  true statement so 8 and 9 are the numbers.