Respuesta :
ANSWER:
The product of two consecutive positive integers is 1332. The larger number is 37.
SOLUTION:
Given, the product of two consecutive positive integers is 1332.
Let the larger number be x.
Then the smaller number is x – 1 [as the given numbers are consecutive]
Product of the two numbers is 1332 → larger number [tex]\times[/tex] smaller number = 1332
x(x – 1) = 1332
(x)x – (x)(1) = 1332
[tex]\begin{array}{l}{x^{2}-x=1332} \\ {x^{2}-x-1332=0}\end{array}[/tex]
This is quadratic equation. let us find the x value by factorization method.
we need to make the two terms product as such that, difference of both numbers should be equal to 1, as x coefficient is 1.
[tex]x^{2}-x-2 \times 666=0[/tex]
keep doing this until we get the difference equals to 1.
[tex]x^{2}-x-4 \times 333=0[/tex]
[tex]\mathrm{x}^{2}-\mathrm{x}-12 \times 111=0[/tex]
[tex]x^{2}-x-36 \times 37=0[/tex]
we got difference 1 that is 37 – 36 = 1
writing the x coefficient in terms of those numbers (36, 37)
[tex]\mathrm{x}^{2}-(37-36) \mathrm{x}-36 \times 37=0[/tex]
[tex]x^{2}-37 x+36 x-36 \times 37=0[/tex]
now, take the common terms
x(x – 37) + 36(x – 37) = 0
(x – 37)(x + 36) = 0
x – 37 = 0 or x + 36 = 0
x = 37 or -36
we can neglect -36, because given numbers are positive numbers.
Hence, the larger number is 37
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.
