Question 991069

Let {{{x}}} = first number (smaller)
Let {{{x + 1}}} = second number (larger) 

given:

{{{x(x+1)=72}}}

{{{x^2+x=72}}}

{{{x^2+x-72=0}}}.............factor completely

{{{x^2+9x-8x-72=0}}}

{{{(x^2+9x)-(8x+72)=0}}}

{{{x(x+9)-8(x+9)=0}}}

{{{(x-8)(x+9) = 0}}}

solutions:

{{{(x-8)= 0}}}=>{{{x=8}}}

{{{(x+9) = 0}}}=>{{{x=-9}}}=> disregard,we need two consecutive {{{positive}}} numbers

so, first number is {{{x=8}}} and second number is {{{x+1=9}}}