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-Dominant- [34]
3 years ago
11

The product of two consecutive positive integers is 1111 more than their sum. find the integers.

Mathematics
1 answer:
Alex787 [66]3 years ago
5 0
The correct question is
<span>The product of two consecutive positive integers is 11 more than their sum. find the integers.

Let
x-------> the first </span>positive integer
x+1-----> the second consecutive positive integer

we know that
x*(x+1)=11+(x+(x+1))----> x²+x=11+(2x+1)----> x²+x=2x+12
x²-x-12=0

using a graph tool------> to resolve the second order equation
see the attached figure

the solution is
x=4

therefore

the numbers are
x=4
x+1=5

the answer is
the numbers are 4 and 5

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The 38th term of 459,450,441,.. will be:

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Step-by-step explanation:

Given the sequence

459,450,441,..

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

computing the differences of all the adjacent terms

450-459=-9,\:\quad \:441-450=-9

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a_1=459

so the nth term will be

a_n=-9\left(n-1\right)+459

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Putting n=38 to find the 38th term

a_n=-9n+468

a_{13}=-9\left(13\right)+468

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a_{13}=351

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