Question

what is the largest of three consecutive postive integers if the product of the small two integers is 11 more than five times the largest integer

Answer 1

Explanation:

The product of the two smaller integers is given as:

(x)(x + 1)

The condition states that this product is 11 more than five times the largest integer:

(x)(x + 1) = 5(x + 2) + 11

Now, let's solve the equation to find the value of "x":

Expand the left side:

x^2 + x = 5x + 10 + 11

Simplify:

x^2 + x = 5x + 21

Move all terms to one side of the equation:

x^2 + x - 5x - 21 = 0

Combine like terms:

x^2 - 4x - 21 = 0

Now, we can factor the quadratic equation:

(x - 7)(x + 3) = 0

Setting each factor to zero and solving for "x":

x - 7 = 0

x = 7

x + 3 = 0

x = -3 (but we are looking for positive integers, so we discard this solution)

The largest of the three consecutive positive integers is x + 2:

7 + 2 = 9

So, the largest integer is 9.