Question 390059

given:

the three consecutive positive even integers 

Assign variables :

    Let {{{x}}} be the first consecutive positive even integers 

    {{{x + 2 }}} be the  second consecutive positive even integers 

   {{{ x + 4}}} be the third consecutive positive even integers 

the product of the first and second is {{{64}}} less than the square of the third

{{{x*(x+2) + 64= (x+4)^2}}}

{{{x^2+2x + 64= x^2+8x + 16}}}

{{{cross(x^2)+2x + 64= cross(x^2) +8x + 16}}}

 {{{2x + 64= 8x + 16}}}

{{{64 - 16 = 8x - 2x}}}

{{{48 = 6x }}}...or

{{{6x =  48 }}}

{{{x =  48/6 }}}

{{{x =  8 }}}.....................the first consecutive positive even integer


  {{{x + 2 = 8 + 2 = 10}}}

{{{x + 2 =  10}}}..............the  second consecutive positive even integer

{{{x + 4 = 8 + 4 = 12}}}

{{{x +4 =  12}}}...............the third consecutive positive even integer


check:

{{{x*(x+2) + 64= (x+4)^2}}}
{{{8*(8+2) + 64= (8+4)^2}}}

{{{8*(10) + 64= (12)^2}}}

{{{80 + 64= 144}}}

{{{144= 144}}}