Answer to Question #129117 in Algebra for uno

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