Question

the product of two consecutive odd no. is 63 .find the no.

Answer 1

Since the difference between odd numbers is 2,
First number: x
Second number: x + 2

Make an equation and solve it,
x(x + 2) = 63
x² + 2x = 63
x² + 2x - 63 = 0

Factorise the equation,
(x - 7)(x + 9) = 0

x - 7 = 0
x = 7

x + 9 = 0
x = -9

So there are two answers for x: 7 and -9.

Now find x + 2, which will have two answers also.

7 + 2 = 9 [First answer]

-9 + 2 = -7 [Second answer]

Therefore, to answer your question, the numbers are 7 and 9 (or -9 and -7).

Answer 2

Answer:

This question can have two answers which are as follows -

1. - 9 and - 7

2. 7 and 9

Step-by-step explanation:

Since the consecutive odd number differ by 2, we may assume the numbers as follow:

First Consecutive Odd Number, m = ' x '

Second Consecutive Odd Number, n = ' x + 2 '

Hence on reading the question carefully we may derive the following relation :

m * n = 63

x * ( x + 2 ) = 63

Simplifying further,

x ^ 2 + 2x = 63

x ^ 2 + 2x - 63 = 0

x ^ 2 + 9x - 7x - 63 = 0

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

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

By zero product rule,

=> x + 9 = 0 OR => x - 7 = 0

=> x = - 9  OR => x = 7

Taking x = - 9,

First Consecutive Odd Number = - 9

Second Consecutive Odd Number = ( - 9 + 2 ) = - 7

Taking x = 7,

First Consecutive Odd Number = 7

Second Consecutive Odd Number = ( 7 + 2 ) = 9