Question

PLEASE HELP ME I'M LOST

The product of two consecutive positive integers is 1,332. Explain how you can write and solve a quadratic equation to find the value of the larger integer.

Answer 1

x - the larger integer (x>0)

x-1 - the smaller integer (the difference between two consecutive integers is always 1)

The product of two consecutive positive integers is 1,332

so:

x•(x -1 ) = 1332

x² - x = 1332

x² - x - 1332 = 0 ⇒ a = 1, b = -1, c = -1332

`x=(-b\pm√(b^2-4ac))/(2a)=(-(-1)\pm√(1^2-4\cdot1\cdot(-1332)))/(2\cdot1)=(1\pm√(1+5328))/(2)\\\\\\x_1=(1+√(5329))/(2)=(1+73)/(2)=37\\\\x_2=(1-√(5329))/(2)\ \\ot>\ 0`

x = 37

Answer 2

The numbers can be written as x and x + 1. Set the product of the numbers equal to 1,332 to get x(x + 1) = 1,332. You can solve the quadratic equation by using the quadratic formula, completing the square, or factoring. When you solve the quadratic equation, you find that x = –37 and 36. Since the question asked for positive integers, the only viable solution is x = 36. To solve for the larger integer, you add 1 to 36 to get an answer of 37.

Explanation:

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