Question

If the product of the sum of two consecutive odd numbers and the difference of these two numbers is 448, find these two odd numbers.

Answer 1

Answer :-

Let the two numbers be x and x + 2

Sum of numbers = x + x + 2 = 2x + 2

Difference = x + 2 - x = 2

According to the question :-

→ Sum of numbers × Difference of numbers = 448

→ ( 2x + 2 ) × 2 = 448

→ 2x + 2 = 448 / 2

→ 2x + 2 = 224

→ 2x = 224 - 2

→ 2x = 222

→ x = 222 / 2

→ x = 111

Hence, two numbers are 111 and 113.

Verification :-

→ Sum of numbers = 111 + 113 = 224

→ Difference = 113 - 111 = 2

According to the question :-

Sum of numbers × Difference of numbers = 448

→ LHS = 224 × 2

→ LHS = 448

→ RHS = 448

LHS = RHS

Hence verified.

Answer 2

Answer:

Given :-

Product of sum of two consecutive odd numbers and the difference of these two numbers is 448,

To Find :-

Odd number

Solution :-

Let the numbers be

$\bf \: y$

and

$\bf \: y + 2$

Now,

According to the question

Their sum will be

$\bf \: y + y + 2 = 2y + 2$

And their difference

$\sf \: y + 2 - y$

Cancellation of y

$2$

$\sf \: 2(2y + 2 ) = 448$

$\sf \: 4y + 4 = 448$

$\sf \: 4y = 448 - 4$

$\sf \: 4y = 444$

$\sf \: y \: = \dfrac{444}{4}$

$\sf \: y = 111$

Numbers are

$\dag{ \textsf{ \textbf{ \underline{y = 111}}}}$

$\dag { \textsf{ \textbf{ \underline{y + 2 = 113}}}}$