Two consecutive positive integers have a product of 110. What are the integers

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annieptl annieptl · Answer 1 · 2018-06-08T21:02:57+02:00

lets call the first number x and the second x+1.
x + ( x + 1 ) =110
2x + 1 = 110
2x = 109
x = 54.5
therefore the two numbers are 54.5 and 55.5

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aksnkj aksnkj · Answer 2 · 2021-10-02T19:58:02+02:00

Answer:

The numbers will be 10 and 11.

Step-by-step explanation:

It is given that the product of two consecutive positive integers is 110.

Let the integers be

[tex]x[/tex]

and

[tex]x + 1[/tex]

Now, the product of the numbers can be written as,

[tex]x(x + 1) = 110 \\ {x}^{2} + x = 110 \\ {x}^{2} + x - 110 = 0[/tex]

Solve the above quadratic equation as,

[tex] {x}^{2} + 11x - 10x - 110 = 0 \\ x(x + 11) - 10(x + 11) = 0 \\ (x + 11)(x - 10) = 0[/tex]

Solve for x as,

[tex]x - 10 = 0 \\ x = 10 \\ x + 11 = 0 \\ x = - 11[/tex]

Now, the integers are positive and hence, the value of x will be 10.

Therefore, the numbers will be 10 and 11.

For more details, refer the link:

https://brainly.com/question/2925460?referrer=searchResults