Question

find the three postive consecutive integers such that the product of the smallest and the largest is 17 more than 3 times the median intger

Answer 1

find the three postive consecutive integers such that the product of the smallest and the largest is 17 more than 3 times the median intger

Answer 2

Answer: 5, 6, 7

Explanation:

Let three positive consecutive integers equal to x, x+1, x+2

Hence,

`\displaystyle\\x(x+2)-3(x+1)=17\\x^2+2x-3x-3=17\\x^2-x-3-17=17-17\\x^2-x-20=0\\x^2-5x+4x-20=0\\x(x-5)+4(x-5)=0\\(x-5)(x+4)=0\\x-5=0\\x-5+5=0+5\\x=5\in\ (x > 0)\\x+4=0\\x+4-4=0-4\\x=-4\\otin\ (x > 0)\\5+1=6\\5+2=7`