SOLUTION: Three consecutive positive integers such that the sum of the square of the first and the product the product of the other two is 46, find the integers.

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Question 499537: Three consecutive positive integers such that the sum of the square of the first and the product the product of the other two is 46, find the integers.
Answer by mananth(16946) About Me  (Show Source):
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let the integers be x, x+1,x+2
x^2+(x+1)(x+2)=46
x^2+x^2+3x+2=46
2x^2+3x-44=0
Find the roots of the equation by quadratic formula

a= 2 ,b= 3 ,c= -44

b^2-4ac= 9 + 352
b^2-4ac= 361
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2B21%29%2F%2812%29
x1=( -3 + 19 )/ 4
x1= 4
x2=( -3 -19 ) / 4
x2= -5.5
They are integers 4,5,6