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Find the two positive consecutive odd integers whose product is 63.3 and 217 and 89 and 117 and 9

Sagot :

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.