The product of two consecutive negative integers is 600. What is the value of the lesser integer?
2 answers:
Two consecutive negative integers are n and n+1. We are told that the product of these two integers is 600 so:
n(n+1)=600
n^2+n=600
n^2+n-600=0
n^2+25n-24n-600=0
n(n+25)-24(n+25)=0
(n-24)(n+25)=0, since we are told that n is negative...
n=-25
(...-25(-24)=600 so -25 is the value of the lesser integer)
Prime factors of 600 are 2*2*2*3*5*5
2*2*2*3 = 24
and 5*5 = 25
so the 2 negative integers are -24 and -25
and lesser integer is -25.
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