Find the product of x and y.

If the number x is 3 less than the number y and the sum of the squares of x and y is 29, find the product of x and y.

Answer :

It is given that

x = y – 3 and x² + y² = 29

It can be written as

x – y = – 3

By squaring on both sides

(x – y)² = (-3)²

Expanding using formula

x² + y² – 2xy = 9

Substituting the values

29 – 2xy = 9

By further calculation

-2xy = 9 – 29 = – 20

Dividing by 2

xy = – 20/-2 = 10

So we get

xy = 10

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