Question

there are two numbers such that the sum of the numbers is 48 and their difference is 8 find the difference of their squares ​

Answer 1

x+y=48,x-y=8 (if one is x,& other is y) then,

x=8+y,

8+y+y=48,

8+2y=48,

y=(48-8)/2=20,

x=20+8=28

difference of squares= (28×28)-(20×20)= 784-400=384

Answer 2

Given

• There are two numbers
• The sum of the numbers is 48.
• The difference of the numbers is 8.

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To Find

• Difference of their squares.

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Solution

Let one of the numbers be 'x' and the other be 'y'.

x + y = 48    (i)

x - y = 8      (ii)

Let's take equation (i)

⇒ x + y = 48

⇒ x = 48 - y

With the value of 'x' let's find value of equation (ii)

⇒ (48 - y) - y = 8

⇒ 48 - y - y = 8

⇒ 48 - 2y = 8

⇒ 48 - 8 = 2y

⇒ 40 = 2y

⇒ y = 40 ÷ 2

⇒ y = 20

With the obtained value of 'y' let's find the value of 'x'.

⇒ x + 20 = 48

⇒ x = 48 - 20

⇒ x = 28

∴ x = 28 and y = 20

Now let's find the difference of their squares.

⇒ (28)² - (20)²

⇒ 784 - 400

⇒ 384

∴ The difference of their squares is 384.

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