Question

the difference 2 number is 3 and the difference between there square is 54 what are the numbers​

Answer 1

Answer:-

Let the numbers be x and y. (x > y).

Given:

Difference between the numbers = 3

⟹ x - y = 3

⟹ x = 3 + y -- equation (1)

Also,

Difference between their squares = 54

⟹ x² - y² = 54

Substitute the value of x from equation (1).

⟹ (3 + y)² - y² = 54

• (a + b)² = a² + b² + 2ab

⟹ 3² + y² - 2 * 3 * y - y² = 54

⟹ 9 - 6y = 54

⟹ 9 - 54 = 6y

⟹ 45/6 = y

⟹ 15/2 = y

Substitute the value of y in equation (1).

⟹ x = 3 + 15/2

⟹ x = (6 + 15)/2

⟹ x = 21/2

Therefore, the two required numbers are 15/2 & 21/2.

Answer 2

Given

• The difference 2 number is 3
• The difference between there square is 54

We Find

• Required numbers

We knows

• X - Y = 3

• X² - Y² = 54

We used

Theorm :- (a+b)² = a² + b² + 2ab

According to the question

we substitute the value of x ( From equation )

= 3² + y² - 2×3×y - y² = 54

= 9 - 6y = 54

= 6y = 54 - 9

= 6y = 45

= y = 45/6

= y = 15/2

And We substitute the value of y ( From equation )

= x = 3 + 15/2

= x = (6+15)/2

= x = 21/2

So, Required numbers is 21/2 and 15/2.

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