Question

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

Answer 1

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

`x(x+2)=63`

Or

`x^2+2x-63=0`

which can be factorized as follows

`(x+9)(x-7)=0`

Which gives

`\begin{gathered} x=7\text{ or } \\ x=-9 \end{gathered}`

Since x is a positive odd integer,

`x\\e-9\text{ }`

Hence the two required integers are

`\begin{gathered} x=7\text{ and } \\ x+2=9 \end{gathered}`

We can also verify our result as the product of 7 and 9 is 63.

Final Answer: Option D is correct.