Question

Find three consecutive positive integers such that the sum of the square of the first and the product of the other two is 154.

Answer 1

Answer: The numbers are 8,9,10

Step-by-step explanation:

let the numbers be x,x+1,x+2

By the condition,

x²+[(x+1)(x+2)]=154

∴ x²+(x²+2x+x+2)=154

∴ x²+(x²+3x+2)=154

∴ 2x²+3x+2=154

∴ 2x²+3x-152=0

∴ 2x²-16x+19x-152=0

∴ 2x(x-8)+19(x-8)=0

∴(2x+19)(x-8)=0

∴2x+19=0        or   x-8=0

∴x=-19/2        or   x=8

since, the numbers are positive x=8

∴ the numbers are:

x=8

x+1=8+1=9

x+2=8+2=10