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find two consecutive odd integers whose product is 99.​

Sagot :

Given:

Product of two consecutive odd integers is 99.

To find:

The two consecutive odd integers.

Solution:

Let the two consecutive odd integers are x and (x+2).

Product of two consecutive odd integers is 99.

[tex]x(x+2)=99[/tex]

[tex]x^2+2x-99=0[/tex]

Splitting the middle term, we get

[tex]x^2+11x-9x-99=0[/tex]

[tex]x(x+11)-9(x+11)=0[/tex]

[tex](x+11)(x-9)=0[/tex]

[tex]x=-11,9[/tex]

If x=-11, then second odd integer is

[tex]-11+2=-9[/tex]

If x=9, then second odd integer is

[tex]9+2=11[/tex]

Therefore, the two consecutive odd integers are either -11, -9 or 9, 11.

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