The product of two consecutive even integers is 24 . Find the two integers. Answer in the form of paired points with the lowest of the two integers first. Answer?

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Answer 1 · 2018-05-11T06:49:17

The two consecutive even integers #:(4,6) or (-6,-4)#

Let ,
#color(red)(n and n-2# be the two consecutive even integers,where #color(red)(n inZZ#

Product of #n and n-2# is 24

#i.e. n(n-2)=24#

#=>n^2-2n-24=0#

Now, #[(-6)+4=-2 and (-6)xx4=-24]#

#:.n^2-6n+4n-24=0#

#:.n(n-6)+4(n-6)=0#

#:.(n-6)(n+4)=0#

#:.n-6=0 or n+4=0...to[n inZZ]#

#=>color(red)(n=6 or n=-4#

#(i)color(red)(n=6)=>color(red)(n-2)=6-2=color(red)(4)#

So,the two consecutive even integers #:(4,6)#

#(ii))color(red)(n=-4)=>color(red)(n-2)=-4-2=color(red)(-6)#

So,the two consecutive even integers #:(-6,-4)#