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Question
The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.
Solution
Let x and y be the two numbers, then,
x2 + y2 = 13 and xy = 6
(i) (x + y)2 = x2 + y2 + 2xy
= 13 + 2×6
= 13 + 12
= 25
∴ x + y = ± `sqrt25` = ±5
(ii) (x − y)2 = x2 + y2 − 2xy
= 13 − 12
= 1
∴ x − y = ±1
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