Question 189629
Call the consecutive integers
{{{a}}}, {{{a+1}}}, and {{{a+2}}}
The square of the sum of the smaller two is:
{{{(a + a + 1)^2}}}
given:
{{{(2a + 1)^2 = (a + 2)^2 + 144}}}
{{{4a^2 + 4a + 1 = a^2 + 4a + 4 + 144}}}
{{{3a^2 + 4a + 1 = 4a + 148}}}
{{{3a^2 = 147}}}
{{{a^2 = 49}}}
{{{a = 7}}}
{{{a+1 = 8}}}
{{{a + 2 = 9}}}
The three consecutive integers are 7, 8, and 9
check:
{{{(a + a + 1)^2 = (a + 2)^2 + 144}}}
{{{(7 + 8)^2 = 9^2 + 144}}}
{{{225 = 81 + 144}}}
{{{225 = 225}}}
OK