The product of two consecutive odd whole numbers is one less than five times their sum. Find the integers

Answer 1

We can create an algebraic equation based on the information provided in the question.

x is the first whole number

x+2 is the second whole number. We add 2 since it is the next odd number.

x ( x + 2 ) + 1 = 5 ( x + x + 2) This is the equation given the parameters set forth in the problem

x² + 2x + 1 = 5x + 5x + 10 we do the multiplication to remove the parenthesis

x² + 2x + 1 = 10x + 10 we combine expressions

x² - 8x - 9 = 0 we move all expressions to one side of the equation

(x - 9) (x + 1) = 0 we factor the trinomial using the FOIL method

x - 9 = 0 now we solve for each term equal to zero

x = 9

x + 1 = 0 now we solve for the second term equal to zero

x = -1

Therefore, we have 2 solution sets that satisfy the criteria of the question: {-1, 1} and {9,11}