Given: Two positive consecutive odd integers.
Required: To find two positive consecutive odd integers whose product is 63.
Explanation: Let x be a positive odd integer. Then (x+2) is the consecutive positive odd integer. Now according to the question
[tex]x(x+2)=63[/tex]Or
[tex]x^2+2x-63=0[/tex]which can be factorized as follows
[tex](x+9)(x-7)=0[/tex]Which gives
[tex]\begin{gathered} x=7\text{ or } \\ x=-9 \end{gathered}[/tex]Since x is a positive odd integer,
[tex]x\ne-9\text{ }[/tex]Hence the two required integers are
[tex]\begin{gathered} x=7\text{ and } \\ x+2=9 \end{gathered}[/tex]We can also verify our result as the product of 7 and 9 is 63.
Final Answer: Option D is correct.
