Answer: 11, 13
Explanation:
The problem is asking us to find two consecutive integers that have a product of 143. If we call x the greatest of the two numbers, the other number can be written as (x-2). Their product must be equal to 143, so we have
[tex]x(x-2)=143[/tex]
Let's solve the equation:
[tex]x^2 -2x -143 =0[/tex]
this is a second-oder equation that has two real solutions: x=13 and x=-11. We are not interested in the negative solution, so our solution is x=13. Therefore, the two numbers are
x=13
x=13-2=11
The complete equation is [tex]x(x-2)=143[/tex]. And the greater integer is [tex]13[/tex].
Let the consider two positive, consecutive, and odd integers are [tex]x, (x-2)[/tex]
Given, the product of two integers as
[tex]x(x-2)=143\\x^{2}-2x=143\\x^{2} -2x-143=0\\x^{2} -13x+11x-143=0[/tex]
[tex]x(x-13)+11(x-13)=0\\(x-13)(x+11)=0\\x=13, x=-11[/tex]
The negative value of [tex]x[/tex] will be neglected.
So,
[tex]x=13[/tex]
and
[tex](x-2)\\=13-2\\=11[/tex]
Hence, The complete equation is [tex]x(x-2)=143[/tex] and the greater integer is [tex]x=13[/tex].
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