Question

The difference of two numbers is 2,the difference of their square is 28.what is their sum?

Answer 1

Let nos be x and y. x >y.

Then,

x - y = 2 - - - (i)

x^2 - y^2 = 28

(x-y) (x+y) = 28 - - - (ii)

Putting value of x-y from eq (i) :

2(x +y) = 28

x + y = 14

Hence, their sum is 14.

Answer 2

Step-by-step explanation:

The difference of the two numbers is 2

a−b=2

⟹a=b+2

and the difference of their squares is 28.

a2−b2=28

⟹(a−b)(a+b)=28

Substitute (a-b) with 2, and you get

2(a+b)=28

⟹a+b=282

⟹a+b=14.

So the sum is 14, and a=b+2 so the numbers are 8 and 6.

Proof:

8−6=2

82−62

⟹(8−6)(8+6)

⟹2×14=28