Question 1134352


Find {{{3}}} consecutive odd integers if the difference of the squares of the least and greatest is {{{120}}}. 


To determine these integers, we start by letting the first odd integer be {{{x}}}. Then we can represent the three consecutive odd integers as {{{x}}},{{{ x + 2}}}, and {{{x + 4}}}.

the squares of the least and greatest is:{{{x^2}}} and {{{(x + 4)^2}}}

if the {{{difference}}} of the squares of the least and greatest is {{{120}}}, we have

{{{(x + 4)^2-x^2=120}}}

{{{x^2 + 8x+16-x^2=120}}}

{{{cross(x^2) + 8x+16-cross(x^2)=120}}}

{{{ 8x=120-16}}}

{{{ 8x=104}}}

{{{ x=104/8}}}

{{{ highlight(x=13)}}}

then {{{ highlight(x + 2=15)}}}, and {{{highlight(x + 4=17)}}}

your odd integers are: {{{ highlight(13)}}}, {{{ highlight( 15)}}}, and {{{highlight( 17)}}}