Question

the sum of the square of Two numbers Is 225 and the square of their sum is 441

What is the reciprocal of their product

Answer 1

Let the two numbers be x and y

( x + y )² = 441

x² + y² = 225

Therefore;

( x + y )² - ( x² + y² ) = 441 - 225

( x + y)² = ( x + y )(x + y)

= x( x+y) + y(x+y)

= x² +xy +xy +y²

= x² + 2xy + y²

Therefore;

(x² + 2xy + y²) - ( x² + y² ) = 441 - 225

2xy/2 = 216/2

xy = 108

The reciprocal of xy is 1/108