SOLUTION: find three consecutive integers such that the square of the smallest increased by four times the largest is five.

Question 958429: find three consecutive integers such that the square of the smallest increased by four times the largest is five.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your smallest number is x
your next smallest number is x + 1
your largest number is x + 2

the square of the smallest increased by 4 times the largest is equal to 5 means:

x^2 + 4 * (x + 2) = 5

x is the smallest.
x + 2 is the largest.

simplify this equation to get:

x^2 + 4x + 8 = 5

subtract 5 from both sides of this equation to get:

x^2 + 4x + 3 = 0

factor this quadratic equation to get:

x = -3
x = 1

both of those values of x will satisfy the requirements of the problem.

when x = -3, x + 2 = -1.

x^2 + 4 * (x + 2) becomes (-3)^2 + 4 * (-1) which becomes 9 - 4 which becomes 5.

when x = -1, x + 2 = 1.

x^2 + 4 * (x + 2) becomes (-1)^2 + 4 * (1) which becomes 1 + 4 which becomes 5.

both x = -3 and x = -1 satisfy the requirements of the problems.

they are your solutions.

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