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Question
The sum of two numbers is 9 and their product is 20. Find the sum of their (i) Squares (ii) Cubes
Solution
Given sum of two numbers is 9 and their product is 20.
Let the numbers be a and b.
a + b = 9
ab = 20
Squaring on both sides gives
(a+b)2 = 92
a2 + b2 + 2ab = 81
a2 + b2 + 40 = 81
So sum of squares is 81 - 40 = 41
Cubing on both sides gives
(a + b)3 = 93
a3 + b3 + 3ab(a + b) = 729
a3 + b3 + 60(9) = 729
a3 + b3 = 729 - 540 = 189
So the sum of cubes is 189.
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