Question

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Answer 1

Answer:

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Answer 2

Answer

One number = 30

Other number = 18

Given

The sum of two positive numbers is 48 and

difference of their squares is 576

To Find

The numbers

Solution

Let one number be , " x "

and other be , " y "

A/c , " The sum of two positive numbers is 48 "

⇒ x + y = 48 ... (1)

A/c , " Difference of their squares is 576 "

⇒ x² - y² = 576

__________________

|     we know that ,               |

|   a² - b² = ( a + b ) ( a - b )   |

_________________

⇒ ( x + y ) ( x - y ) = 576

⇒ ( 48 ) ( x - y ) = 576   [ From  (1) ]

⇒ x - y = 12 ... (2)

On solving (1) + (2) , we get ,

⇒ ( x + y ) + ( x - y ) = 48 + 12

⇒ x + y + x - y = 60

⇒  2x = 60

⇒  x = 30

On sub. x value in (1) , we get ,

⇒ 30 + y = 48

⇒ y = 48 - 30

⇒ y = 18

So , One number , x = 30

and other number , y = 18

Verification

Sub. x and y values in (1) and (2) .

So , Let's take eq (1) ,

⇒ LHS

⇒ x + y

⇒ 30 + 18

⇒ 48

⇒ RHS

Hence proved

Now , eq (2) ,

⇒ LHS

⇒ x² - y²

⇒ (30)² - (18)²

⇒ 900 - 324

⇒ 576

⇒ RHS

Hence proved