Question

The product of two consecutive odd integers is 63 find all such pairs of integers

Answer 1

Hi there!

Let the two consecutive odd integers be " x + 1 " and " x + 3 "

Accr'ding to the question :-

(x + 1) (x + 3) = 63

=> x² + 4x + 3 = 63

=> x² + 4x + 3 - 63 = 0

=> x² + 4x - 60 = 0

=> x² + 10x - 6x - 60 = 0

=> x (x + 10) - 6 (x + 10) = 0

=> (x + 10) (x - 6) = 0

∴ x = 6 Or x = - 10

Hence,
The two consecutive numbers are :-

" For x = 6 "

• x + 1 = 6 + 1 = 7
• x + 3 = 6 + 3 = 9

" For x = - 10 "

• x + 1 = - 10 + 1 = - 9
• x + 3 = - 10 + 3 = - 7

~ Hope it helps!

Answer 2

x= first consecutive odd integer
x+2= second consecutive odd integer
product= multiply


x(x + 2)= 63
multiply x by all terms in parentheses

(x*x) + (x*2)= 63
multiply in parentheses

x^2 + 2x= 63
subtract 63 from both sides

x^2 + 2x - 63= 0
factor

(x + 9)(x - 7)= 0
set each parentheses equal to 0

x + 9= 0
x= -9

x - 7= 0
x= 7

-9 and 7 could each be the first consecutive odd integer. Add 2 to each to find the second consecutive odd integer.


ANSWER: since the question did not say if the integers were positive or negative, the possible pairs of consecutive odd integers are:

x= -9; x + 2= -7

x= 7; x + 2= 9

Hope this helps! :)