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find 3 positive consecutive integers such that the product of the first and the third integer is 17 more than three times the second integer

 Apr 5, 2022
 #1
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The numbers are: 5,  6,  7

 

5 x 7 ==3 x 6 + 17 ==35 == 35

 Apr 5, 2022
 #2
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Let the 3 numbers be \(x, x+1, x+2\)

 

We have the equation: 

\(x(x+2)=17+3(x+1)\)

Simplifying into a quadratic:

\(x^2 - x - 20 = 0\)

Factor:

\((x+4)(x-5) = 0\)

 

We want x to be positive, so x must equal 5, meaning the 3 integers are \(\color{brown}\boxed{5,6,7}\)

 Apr 5, 2022

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