Question

4. The sum
of two numbers is 12 and difference of their squares is 12. Find the difference of the numbers.​

Answer 1

Let the two numbers be x and y

given that the sum of two numbers is 12

i.e.

x+y = 12 - (1)

and, the difference between their squares is 12

i.e.

x^2-y^2 = 12

(x+y)(x-y) = 12 [using the identity a^2 - b^2 = (a+b)(a-b)]

using the value of x+y in above

12(x-y) = 12

x-y = 1

Answer 2

Answer:

The difference is 1.

x = 13/2                |             y = 11/2

Step-by-step explanation:

Let the two numbers be x and y.

Given that, x + y = 12   -----------(1)

                  x² - y² = 12

By using identity: a² - b² = (a + b)(a - b)

x² - y² = (x + y)(x - y)

12 = 12(x - y)

12/12 = x - y

x - y = 1      ------------(2)

By adding equations (1) and (2)

(x + y) + (x - y) = 12 + 1

x + y + x - y = 13

2x = 13

x = 13/2

By putting value of x in equation (1)

x + y = 12

13/2 + y = 12

y = 12 - 13/2

y = (24 - 13)/2

y = 11/2

x = 13/2, y = 11/2

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