Question

The sum of two numbers is 21 and the sum of their squares is 261, Find the numbers

Answer 1

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Answer 2

Let the two numbers be x an y

x + y = 21

=> y = 21 - x ----> (1)

According to the question,

x² + y² = 261

putting equation (1) in y;

=> x² + (21-x)² = 261

=> x² + 441 + x² - 42x = 261

=> 2x² - 42x + 180 = 0

=> x² - 21x + 90 = 0

=> x² - 6x - 15x + 90 = 0

=> x(x - 6) - 15(x - 6) = 0

=> (x - 15) (x - 6) = 0

=> x = 15, 6

Let x be the greater number,

So x = 15

and y = 21 - x = 21 - 15

=> y = 6