Formulate and solve problems involving quadratic equations

Question

The largest of three consecutive positive numbers is X. the square of this number (X) exceeds the sum of the other two numbers by 38. Determine the values of these numbers

Answer 1

The largest of three consecutive positive numbers is x, so the numbers are (x-2), (x-1), and x.  The square of this number (x) exceeds the sum of the other two numbers by 38:

 

x² = (x-2) + (x-1) + 38

x² = 2x + 35

x² - 2x - 35 = 0

 

Factors to:

 

(x-7)(x+5) = 0

x = 7 and -5

 

Since the problem states that a is positive number, the answer is x = 7

 

Check:

x² = (x-2) + (x-1) + 38

7² = 5 + 6 + 38

49 = 49

Check!