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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.

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unicorn3125

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

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-1)\pm\sqrt{1^2-4\cdot1\cdot(-1332)}}{2\cdot1}=\dfrac{1\pm\sqrt{1+5328}}{2}\\\\\\x_1=\dfrac{1+\sqrt{5329}}{2}=\dfrac{1+73}{2}=37\\\\x_2=\dfrac{1-\sqrt{5329}}{2}\ \not>\ 0[/tex]

x = 37

CT0723

Answer:

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.

Step-by-step explanation:

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