The sum of the squares of two numbers is 545 and the square of their difference is 1. Find the product of the two numbers.

Correct option is D

Given:

The sum of the squares of two numbers is 545.

The square of their difference is 1.

Formula Used:

​$$(x + y)^2 = x^2 + y^2 + 2xy$$​​

​$$(x - y)^2 = x^2 + y^2 - 2xy$$​​

Solution:

Let the two numbers be x and y.

Sum of squares: $$x^2 + y^2 = 545$$​​

Square of the difference: $$(x - y)^2 = 1$$

​$$x^2 + y^2 = 545$$​​

​$$(x - y)^2 = 1$$​​

​$$(x - y)^2 = x^2 + y^2 - 2xy = 1$$​​

Substituting $$x^2 + y^2 = 545$$​ into this:

545 - 2xy = 1

2xy = 544

xy = $$\frac{544}{2} = 272$$​​

The product of the two numbers is 272

Thus, the correct option is (d) 272