The product of two consecutive room numbers is 380380. find the room numbers

They are consecutive hence they can be written in this form x,x+1
product of the two rooms is 380380
x(x+1)=380380


subtracting 380380 from both sides

using the quadratic formula


x=616.2497 is room number1 x=617.2497 is room 2
but if you meant 380 instead of 380380
the equation will be

the room numbers will exactly be 19,20

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