Question

Q
is
uur
Find
differences
The difference of two number is 14 and the difference
in their
Square is 448 find the solution
[hint(x-y)2 = (x+y) 2 - 4xy]​

Answer 1

GIVEN:

• The difference between two number is 14.
• The difference between their Square is 448

TO FIND:

• What are the two numbers ?

SOLUTION:

Let the one number be 'x'

and

another number be 'y'

CASE:- 1)

❐ The difference between two number is 14.

According to question:-

➠ x – y = 14....❶

CASE:- 2)

❐ The difference between their Square is 448.

According to question:-

➠ x² – y² = 448

Put the value of 'x' from equation 1)

➠ (14+y)² – y² = 448

From identity

• (a+b)² = a² + 2ab + b²

➠ 196 + 28y + $\sf{\cancel{y^2}}$ – $\sf{\cancel{y^2}}$ = 448

➠ 28y = 448-196

➠ 28y = 252

➠ y = $\sf{\cancel\dfrac{252}{28}}$

➠ ★ y = 9 ★

Put the value of 'y' in equation 1)

➠ x – 9 = 14

➠ x = 14+9

➠ ★ x = 25 ★

❝ Hence, the two numbers are 9 and 25 ❞

______________________

Answer 2

Solution :

Let the two number's be r & m;

A/q

$\longrightarrow\sf{r-m=14.....................(1)}$

&

$\longrightarrow\sf{(r)^{2} -(m)^{2}=448}\\\\\longrightarrow\sf{(r+m)(r-m)=448\:\:\:[\therefore formula\:a^{2} - b^{2}]}\\\\\longrightarrow\sf{(r+m)(14)=448\:\:[from(1)]}\\\\\longrightarrow\sf{r+m=\cancel{448/14}}\\\\\longrightarrow\sf{r+m=32}\\\\\longrightarrow\sf{r=32-m.........................(2)}$

∴ Putting the value of r in equation (1),we get;

$\longrightarrow\sf{32-m-m=14}\\\\\longrightarrow\sf{32-2m=14}\\\\\longrightarrow\sf{-2m=14-32}\\\\\longrightarrow\sf{-2m=-18}\\\\\longrightarrow\sf{m=\cancel{-18/-2}}\\\\\longrightarrow\bf{m=9}$

∴ Putting the value of m in equation (2),we get;

$\longrightarrow\sf{r=32-9}\\\\\longrightarrow\bf{r=23}$

Thus;

The two number's will be 23 & 9 .